Assignment1 for chapter 1
国贸作业1
Assignment 1CHAPTER 2EARLY TRADE THEORIES:Mercantilism and the Transition to the Classical World of David RicardoPart 1. Multiple-Choice Questions (only one answer is right)1. In the price-specie-flow doctrine, a deficit country will __________ gold, and this goldflow will ultimately lead to __________ in the deficit country’s exports.a. lose; a decreaseb. lose; an increasec. gain; a decreased. gain; an increase2. In the Mercantilist view of international trade (in a two-country world),a. both countries could gain from trade at the same time, but the distribution of the gainsdepended upon the terms of trade.b. both countries could gain from trade at the same time, and the terms of trade were ofno consequence for the distribution of the gains.c. neither country could ever gain from trade.d. one country’s gain from trade was associated with a loss for the other country.3. According to the labor theory of value,a. the value of labor is determined by its value in production.b. the value of a good is determined by the amount of labor with which each unit ofcapital in an industry works.c. the price of a good A compared to the price of good B bears the same relationship asthe relative amounts of labor used in producing each good.d. the values of two minerals such as coal and gold with similar production costs may bevery different.4. If the demand for traded goods is price-inelastic, the price-specie-flow mechanism will1result ina. gold movements between countries that remove trade deficits and surpluses.b. gold movements between countries that worsen trade deficits and surpluses.c. negligible movements of gold between countries and hence little or no adjustment oftrade deficits and surpluses.d. a removal of the basis for trade between countries.5. In Adam Smith’s view, international tradea. benefited both trading countries.b. was based on absolute cost differences.c. reflected the resource base of the countries in question.d. all of the above.6. Which of the following policies would NOT be consistent with the Mercantilist balance-of-trade doctrine?a. payment of high wages to laborb. import duties on final productsc. export subsidiesd. prohibition of imports of manufactured goods7. During the price-specie-flow adjustment process to a trade imbalance, if demands forgoods are inelastic, then, when the price level __________ in the country with the trade deficit, the value of that country’s exports will __________ as the price-specie-flowprocess takes place.a. falls; increaseb. falls; decreasec. rises; increased. rises; decrease8. David Hume’s price-specie-flow mechanisma. reinforced the Mercantilist notion that a country could maintain a permanent“favorable” balance of trade where exports exceeded imports.b. works more effectively if demands for traded goods are “price-elastic” rather than“price-inelastic.”c. assumed that the countries involved have substantial unemployment.d. works equa lly effectively whether demands for traded goods are “price-elastic” or“price-inelastic.”29. The price-specie-flow mechanism suggested thata. a country could easily maintain a balance-of-payments surplus for a long period oftime.b. a deficit country would experience an increase in its money supply and its price level.c. a surplus country would experience an increase in its money supply and its price level.d. a country’s internal price level has no relation to the country’s foreign trade activities.10. The policy of minimum government interference in or regulation of economic activity,advocated by Adam Smith and the Classical economists, was known asa. the law of comparative advantage.b. laissez-faire.c. the labor theory of value.d. Mercantilism.11. A Mercantilist policymaker would be in favor of which of the following policies orevents pertaining to his/her country?a. a decrease in the size of the populationb. a minimum wage bill to protect the standard of living of workersc. a prohibition on the export of manufactured goodsd. an increase in the percentage of factors of production devoted to adding value toimported raw materials in order to later export the resulting manufactured goods. 12. In the context of David Hume’s price-specie-flow mechanism that challenged thefeasibility of the Mercantilist ideas regarding a trade surplus, which one of the following statements is NOT correct?a. There is a decrease in the money supply in the deficit country.b. There is an increase in the price level in the surplus country.c. There is an increase in real income in the surplus country.d. Price changes in the surplus country cause that country’s exports to decrease.13. In David Hume’s price-specie-flow doctrine or adjustment mechanism, the assumption ismade that changes in the money supply have an impact on __________. Further, thedemand for traded goods is assumed to be __________ with respect to price.a. prices rather than on output; elasticb. prices rather than on output; inelasticc. output rather than on prices; elasticd. output rather than on prices; inelastic14. The “paradox of Mercantilism” reflected that fact that3a. trade surpluses were fostered by protective tariffs.b. rich countries were comprised of large numbers of poor people.c. gold inflows led to higher prices and reduced exports.d. gold could not be hoarded and provide money for the economy at the same time.15. Given the following Classical-type table showing the number of days of labor inputrequired to obtain one unit of output of each of the two commodities in each of the twocountries:bicycles computersUnited States 4 days 3 daysUnited Kingdom 5 days 6 daysThe United States has an absolute advantage in the production of __________.a. bicycles (only)b. computers (only)c. both bicycles and computersd. neither bicycles nor computers16. With M S = supply of money, V = velocity of money, P = price level, and Y = real output,which one of the following indicates the quantity theory of money expression?a. M S Y = PVb. M S P = VYc. M S = PY - Vd. M S V = PY17. In the price-specie-flow mechanism, there is a gold __________ a country with a balance-of-trade surplus, and this gold flow ultimately leads to __________ in the surpluscountry’s exp orts.a. inflow into; an increaseb. inflow into; a decreasec. outflow from; an increased. outflow from; a decrease18. In the price-specie-flow adjustment mechanism, a country with a balance-of-trade surplusexperiencesa. a gold inflow and a decrease in the price level.4b. a gold outflow and an increase in the money supply.c. an increase in the money supply and a decrease in exports.d. a decrease in the money supply and a decrease in imports.19. Suppose that country A’s total exports are 10,000 units of good X at a price of $20 perunit, meaning that country A’s export earnings or receipts are $200,000. Suppose alsothat the foreign price elasticity of demand for country A’s exports of good X is (-) 0.6. If country A’s prices for all goods, including its exports, now rise by 10% because of a gold inflow such as in the Mercantilist model, then, other things equal, country A’s exports of good X will fall by __________ and country A’s export earni ngs or receipts will become __________.a. 600 units; less than $200,000b. 600 units; greater than $200,000c. 1,000 units; less than $200,000d. 1,000 units; greater than $200,000Part 2 DefinitionMercantilismCHAPTER 3THE CLASSICAL WORLD OF DAVID RICARDO AND COMPARATIVE ADVANTAGEPart 1. Multiple-Choice Questions1. In the following Classical-type table showing the output per 10-days of labor input in eachof the two commodities in each of the two countries,Cameras Wine5France 100 units 40 unitsGermany 150 units 50 unitsa. Germany has a comparative advantage in both goods.b. France has an absolute advantage in both goods.c. France has a comparative advantage in cameras.d. the pretrade price ratio in France is 1 wine = 2.5 cameras.2. Given the following Ricardo-type table shows the labor input required per unit of outputin each of the two industries in each of the two countries:Shirts BrandyUnited States 4 days 12 daysFrance 6 days 12 daysWhich one of the following statements is correct?a. France’s pretrade price ratio is 1 brandy = 2 shirts.b. The U.S. pretrade price ratio is 1 shirt = 3 brandy.c. The United States has an absolute advantage in both goods.d. France will export shirts after trade begins.3. In the situation in Question #2 above, if the countries engage in trade at posttrade prices(terms of trade) of 1 shirt = 0.5 brandy, thena. France gets all the gains from trade.b. the United States gets all the gains from trade.c. neither country gains from trade.d. the two countries share equally in the gains from trade.4. The assumption of constant costs of production in the Classical model results in a__________ production possibilities frontier, and, in the case of a “small” country,__________ specialization in production when trade takes place.a. linear; incompleteb. concave-to-the-origin; completec. convex-to-the-origin; incompleted. linear; complete5. In the Classical (Ricardo) analysis,6a. if a country has an absolute advantage in a good, it also has a comparative advantagein the good.b. if a country has a comparative advantage in a good, it cannot have an absoluteadvantage in the good.c. a country can have a comparative advantage in a good at the same time that it has anabsolute advantage in that good.d. a country with an absolute advantage in all goods cannot gain from trade.6. Given the following Ricardo-type table shows the labor input required per unit of output ineach of the two industries in each of the two countries:Steel ClothUnited Kingdom 4 days 8 daysGermany 6 days 9 daysWhich one of the following statements is true?a. The United Kingdom has an absolute advantage in both goods and a comparativeadvantage in cloth.b. The pretrade price ratio in the United Kingdom is 1 steel:2 cloth.c. The United Kingdom has an absolute advantage in neither good but a comparativeadvantage in steel.d. The pretrade price ratio in Germany is 1 cloth:1.5 steel.7. Given the information in Question #6 above, suppose that Germany is a much larger country in terms of production and income than is the United Kingdom. In this situation, other things equal, when the countries engage in trade, the posttrade price ratio (terms of trade) would tend to settle __________, and __________ would therefore tend to have relatively large gains from trade.a. toward a value of 1 cloth:2 steel; the United Kingdomb. toward a value of 1 cloth:2 steel; Germanyc. toward a value of 1 cloth:1.5 steel; the United Kingdomd. toward a value of 1 cloth:1.5 steel; Germany8. Given the following Ricardo-type table showing the amount of labor input needed to get one unit of output in each industry in each country:Wheat Chairs7Malaysia 3 days 2 daysIndia 10 days 8 daysa. Terms of trade of 1 wheat:1.25 chairs is not a feasible equilibrium terms of trade.b. Terms of trade of 1 wheat:1.5 chairs would give all the gains from trade to India.c. Malaysia has an absolute advantage in both goods and a comparative advantage inwheat.d. India has an absolute advantage in both goods and a comparative advantage in wheat.9. If a country’s relative price of X (compared to Y) in autarky is greater than the s ame relativeprices on the world market, then the country has a comparative advantage in good__________, and it will __________.a. X; export Y and import Xb. X; export X and import Yc. Y; export Y and import Xd. Y; export X and import Y10. As a country moves from autarky to trade, the relative price of the country’s import good will __________ for home consumers, and the relative price of the country’s export good __________ for home consumers.a. fall; will riseb. fall; also will fallc. rise; also will rised. rise; will fall11. Suppose that, in a Classical constant-opportunity-costs framework, country I can produce15 units of wheat if it devotes all of its resources to wheat production and 45 units ofclothing if it devotes all of its resources to clothing production. In a trading situation for this country, if the world price ratio is P wheat/P clothing= ⅓ (or P clothing/P wheat = 3), country Iwoulda. export wheat and import clothing.b. export clothing and import wheat.c. be indifferent to trade.d. export either clothing or wheat and import either wheat or clothing – cannot bedetermined without more information.12. Suppose that, with constant opportunity costs, Spain can produce 2,000 units of clothing ifit devotes all of its resources to clothing production and 8,000 units of wheat if it devotes all of its resources to wheat production. If Spain is opened to trade at a world price ratio of1 wheat:0.4 clothing (or 1 clothing:2.5 wheat), Spain will export __________; if the worldprice ratio were 1 wheat:4 clothing (or 1 clothing:2.5 wheat), Spain would __________.89a. wheat; also export wheatb. wheat; would export clothingc. clothing; also would export clothingd. clothing; would be indifferent to trade13.Given the following constant-cost production-possibilities frontiers for Pakistan and India:Pakistan has an autarky relative price of __________; if trade begins with India, then Pakistan would produce at point __________, assuming complete specialization.a. 1 cloth:0.5 wheat (i.e., P cloth /P wheat = 0.5); Ab. 1 cloth:0.5 wheat (i.e., P cloth /P wheat = 0.5); Bc. 1 cloth:2 wheat (i.e., P cloth /P wheat = 2); Ad. 1 cloth:2 wheat (i.e., P cloth /P wheat = 2); B14. Country A has the following constant-opportunity-costs production-possibilities frontier(PPF):Suppose that this country in autarky is located at point R on its PPF, where it is producing 300 units of good Y and __________ of good X. Suppose that country A is now opened to trade and can trade at a terms of trade of 1X:3Y. Assuming complete specialization inproduction, the country will now produce at __________.a. 50 units; point N and will export good X and import good Yb. 150 units; point N and will export good X and import good Yc. 50 units; point M and will export good Y and import good Xd. 150 units; point M and will export good Y and import good X15. If, in a two-commodity, two-country Classical world, Sweden can make a unit of furniturewith 10 days of labor and a unit of steel with 15 days labor, while Germany can make a unit of furniture with 12 days of labor and a unit of steel with 12 days labor, thena. Sweden has an absolute advantage in steel and Germany has an absolute advantage infurniture.b. Sweden has a comparative advantage in steel and Germany has a comparativeadvantage in furniture.c. the pretrade price ratios indicate that Germany will export steel if trade takes place.d. the pretrade price ratio in Sweden is 1 furniture:1.5 steel.16. Given the following Ricardo-type table showing the amount of labor input required toproduce one unit of output of each of the two goods in each of the two countries:Wheat ClothingUnited Kingdom 6 days 5 daysUnited States 4 days 3 daysa. The United Kingdom has an absolute advantage in neither good.b. The United States has a comparative advantage in wheat.c. The United States has a comparative advantage in both goods.d. A post-trade price ratio (terms of trade) of 1 wheat:1.5 clothing is a feasibleequilibrium post-trade price ratio.17. In Question #16 above,a. if the United Kingdom were a much larger country than the United States, then, otherthings equal, the terms of trade would tend to be located more toward the U.S.pre-trade price ratio than toward the U.K. pre-trade price ratio.b. if world demand (the sum of U.S. demand and U.K. demand) were directed more10toward clothing than toward wheat, other things equal, then the terms of tradewould tend to be located more toward the U.K. price ratio than toward the U.S.pre-trade price ratio.c. a post-trade price ratio (terms of trade) of 1 clothing:0.75 wheat would mean that theUnited Kingdom did not gain from trade.d. a post-trade price ratio (terms of trade) of 1 wheat:1.2 clothing would give all the gainsfrom trade to the United States.18. Which one of the following is NOT an assumption contained in the Classical/Ricardo trademodel?a. Factors of production (labor) are completely mobile within a country.b. Factors of production (labor) are completely mobile between countries.c. Marginal costs are constant as production increases for a firm/industry.d. Transportation costs of goods between countries are zero.19. Suppose that a country in the Classical model has the following production-possibilities frontier (PPF):If, in autarky, the country is producing 700 computers and is located at point Mon the PPF, the country would be producing __________ autos. If the country isnow opened to trade at a terms of trade of 1 auto: 2 computers (or 1 computer: 0.5auto), it would export __________.a. 120; autos;b. 120; computers;c. 280; autos;d. 280; computers20. In Question #19 above, suppose that the country, when it is opened to trade, did not11change its production combination from the production combination at point M. In this situation, how many units of its import good could the country obtain if it exported all of the export good that it produced?a. 240 units;b. 350 units;c. 500 units;d. 800 units;Part 2 DefinitionProduction-possibility frontier (PPF)CHAPTER 4EXTENSIONS AND TESTS OF THE CLASSICAL MODEL OF TRADE Part 1. Multiple-Choice Questions1. Suppose that, in a Classical model with two goods, Germany can produce 50 units of steelwith one day of labor and 30 units of textiles with one day of labor; Switzerland canproduce 45 units of steel with one day of labor and 45 units of textiles with one day of labor.If the exchange rate is fixed at 1 Swiss franc = 1 euro and if the Swiss wage rate is 10francs per day, then, in trading equilibrium, German wagesa. must be greater than 10 euros per day.b. must be less than 10 euros per day.c. must be equal to 10 euros per day.d. can be above, below, or equal to 10 euros per day – cannot be determined withoutmore information.2. You are given the following Classical-type table indicating the number of days of laborinput needed to make one unit of output of each of the five commodities in each of thetwo countries. Assume that the wage rate in England is £20 per day, that the wage rate in Portugal is 40 euros per day, and that the fixed exchange rate is £1 = 3 euros.Good A Good B Good C Good D Good E12England 1 day 5 days 2 days 1 day 4 daysPortugal 4 days 4 days 1 day 2 days 5 daysWith the given information, what will be the trade pattern if the two countries engage in trade?a. England will export good A and import goods B, C, D, and E.b. England will export goods A and D and import goods B, C, and E.c. England will export goods A, B, and E and import goods C and D.d. England will export goods A, B, D, and E and import good C.3. In Question #2 above, suppose that one-half day of labor must be used to transport agood internationally, no matter which good is considered and which country is doing the exporting. With this addition of transportation costs, England will export good(s)__________ and will import good(s) __________.a. A; B, C, D, and Eb. A and D; B, C, and Ec. A; B, C, and Ed. A; B and C4. You are given the following Classical-type table showing the output of 10 days labor in theproduction of each of the two commodities in each of the two countries. Assume thatthe U.K. worker’s wage is £30 per day and that the fixed exchange rate is $2 = £1.Food ClothingUnited States 30 units 30 unitsUnited Kingdom 20 units 15 units. If trade is taking place between the two countries, what is the “upper limit” to the U.S.worker’s wage per day?a. $30;b. $40;c. $90;d. $1205. In the situation in Question #4 above, if trade is taking place, what is the lower limit” tothe U.S. worker’s wage per day?a. $30;b. $40 ;c. $90;d. $1206. Given the following Classical-type table shows the number of days of labor inputrequired to obtain one unit of output of each of the three commodities in each of the two countries:13good T good X good YUnited Kingdom 4 days 5 days 3 daysUnited States 4 days 4 days 2 daysSuppose that the wage rate in the United Kingdom is £30 per day, the wage rate in theUnited States is $40 per day, and the exchange rate is £1 = $1. In this situation, theUnited Kingdom willa. export good T and import goods X and Y.b. export good Y and import goods T and X.c. export goods T and X and import good Y.d. export goods X and Y and import good T.7. In Question #6 above, if the U.S. wage rate is $40 per day and the exchange rate is £1 =$1, what is the upper limit to the wage rate in the United Kingdom that is consistent with two-way trade between the countries?a. £26⅔ per day;b. £30 per day;c. £32 per day;d. £40 per day8. In a Ricardo-type model, if Portuguese workers can produce three times as much wine perday as English workers but only twice as much cloth per day as English workers, then, if Portuguese wages are 30 euros per day, the upper limit to English wages per day is__________. (Assume 1 euro = £1.)a. £10 ;b. £15 ;c. £60;d. £909. The following Classical-type table shows the number of days of labor input required toobtain one unit of output of each of the two commodities in each of the three countries:clothing wheatSpain 3 days 6 daysUnited States 2 days 5 daysEngland 4 days 6 daysGiven this information, the United States has an absolute advantage over Spain ina. both goods, and the United States also has an absolute advantage over England inboth goods.b. both goods, but the United States has an absolute advantage over England in neithergood.c. neither good, but the United States has an absolute advantage over England in bothgoods.14d. neither good, and the United States also has an absolute advantage over England inneither good.10. In the three-country world in Question #9, which one of the following statements is TRUE?a. Posttrade prices (terms of trade) of 1 wheat:2.5 clothing (or 1 clothing:0.4 wheat)would give all the gains from trade to the United States.b. Posttrade prices (terms of trade) of 1 wheat:3 clothing (or 1 clothing:⅓ wheat) arepossible.c. At posttrade prices (terms of trade) of 1 wheat:1.6 clothing (or 1 clothing:0.625wheat), England would export wheat and Spain and the United States would exportclothing.d. At posttrade prices (terms of trade) of 1 wheat:2.25 clothing (or 1 clothing:0.44wheat), Spain would export clothing and import wheat.11. In the table in Question #9 above, when trade is taking place among the three countries,__________ will always be exporting wheat and __________ will always be exportingclothing.a. the United States; Englandb. England; the United Statesc. England; Spaind. Spain; the United States12. Given the following Classical-type table showing the fixed money prices of each good ineach of the two countries:Shoes WineUnited States $20/pair $10/bottleSwitzerland 100 francs/pair 40 francs/bottle If the exchange rate is flexible, the upper limit to the price of the dollar (i.e., the number of Swiss francs per dollar above which there is export of both goods by Switzerland) isa. 5 francs = $1;b. 4 francs = $1;c. 0.25 francs = $1;d. 0.20 francs = $1.13. Suppose that the labor requirements per unit of output in each of the two industries ineach of three countries are as follows:Wheat Cloth15Spain 2 days 3 daysFrance 2 days 2 daysUnited States 1 day 3 daysIn this situation, with an international terms of trade of 1 cloth:2 wheat (or 1 wheat:½ cloth), __________ would export cloth and import wheat; if the terms of trade were, instead, 1wheat:¾ cloth (or 1 cloth:1⅓ wheat), __________ would export cloth and import wheat.a. France and the United States; Spainb. Spain and France; Francec. France and the United States; Spain and the United Statesd. Spain and France; Spain and the United States14. Given the following Classical-type table showing the number of days of labor inputrequired to obtain one unit of output of each of the two commodities in each of the threecountries:wine clothingDenmark 4 days 6 daysGermany 3 days 3 daysPortugal 5 days 9 daysWhich one of the following statements is correct?a. If trade is taking place, Germany will always be exporting wine.b. If trade is taking place, Denmark will always be exporting clothing.c. If trade is taking place, Portugal will always be importing clothing.d. If trade is taking place and the terms of trade are 1 clothing:1.6 wine, Germany will beexporting clothing and Denmark and Portugal will be importing clothing.15. Suppose that the wage rate in country A is three times the wage rate in country B. In thissituation, in the context of the Classical/Ricardo trade model, country A would be able to export goods to country B in industries wherea. A’s workers were less than one-third as productive as B’s workers.b. A’s workers were equally as productive as B’s workers.c. A’s workers were less than three times as productive as B’s workers.d. B’s workers were less than one-third as productive as A’s workers.Part 2 Simple Questions1.Suppose the unit production conditions in Spain and UK are as follows:16Please determine which kinds of commodities these two countries should export and import (Suppose the exchange rate is 0.8 pound/euro)2.Suppose the labor requirements in Sweden, Germany and France are as follows:Please tell me which kinds of commodities these three countries should produce and export.17。
线性代数 英文讲义
Chapter 1 Matrices and Systems of EquationsLinear systems arise in applications to such areas as engineering, physics, electronics, business, economics, sociology（社会学）, ecology （生态学）, demography(人口统计学), and genetics（遗传学）, etc. §1. Systems of Linear EquationsNew words and phrases in this section:Linear equation 线性方程Linear system，System of linear equations 线性方程组Unknown 未知量Consistent 相容的Consistence 相容性Inconsistent不相容的Inconsistence 不相容性Solution 解Solution set 解集Equivalent 等价的Equivalence 等价性Equivalent system 等价方程组Strict triangular system 严格上三角方程组Strict triangular form 严格上三角形式Back Substitution 回代法Matrix 矩阵Coefficient matrix 系数矩阵Augmented matrix 增广矩阵Pivot element 主元Pivotal row 主行Echelon form 阶梯形1.1 DefinitionsA linear equation (线性方程) in n unknowns（未知量）is1122...n na x a x a x b+++=A linear system of m equations in n unknowns is11112211211222221122...... .........n n n n m m m n n m a x a x a x b a x a x a x b a x a x a x b+++=⎧⎪+++=⎪⎨⎪⎪+++=⎩ This is called a m x n (read as m by n) system.A solution to an m x n system is an ordered n-tuple of numbers （n 元数组）12(,,...,)n x x x that satisfies all the equations.A system is said to be inconsistent （不相容的） if the system has no solutions.A system is said to be consistent （相容的）if the system has at least one solution.The set of all solutions to a linear system is called the solution set（解集）of the linear system.1.2 Geometric Interpretations of 2x2 Systems11112212112222a x a xb a x a x b +=⎧⎨+=⎩ Each equation can be represented graphically as a line in the plane. The ordered pair 12(,)x x will be a solution if and only if it lies on bothlines.In the plane, the possible relative positions are(1) two lines intersect at exactly a point; (The solution set has exactly one element)(2)two lines are parallel; (The solution set is empty)(3)two lines coincide. (The solution set has infinitely manyelements)The situation is the same for mxn systems. An mxn system may not be consistent. If it is consistent, it must either have exactly one solution or infinitely many solutions. These are only possibilities.Of more immediate concerns is the problem of finding all solutions to a given system.1.3 Equivalent systemsTwo systems of equations involving the same variables are said to be equivalent（等价的，同解的）if they have the same solution set.To find the solution set of a system, we usually use operations to reduce the original system to a simpler equivalent system.It is clear that the following three operations do not change the solution set of a system.(1)Interchange the order in which two equations of a system arewritten;(2)Multiply through one equation of a system by a nonzero realnumber;(3)Add a multiple of one equation to another equation. (subtracta multiple of one equation from another one)Remark: The three operations above are very important in dealing with linear systems. They coincide with the three row operations of matrices. Ask a student about the proof.1.4 n x n systemsIf an nxn system has exactly one solution, then operation 1 and 3 can be used to obtain an equivalent “strictly triangular system ”A system is said to be in strict triangular form (严格三角形) if in the k-th equation the coefficients of the first k-1 variables are all zero and the coefficient ofkx is nonzero. (k=1, 2, …,n)An example of a system in strict triangular form:123233331 2 24x x x x x x ++=⎧⎪-=⎨⎪=⎩Any nxn strictly triangular system can be solved by back substitution (回代法).(Note: A phrase: “substitute 3 for x ” == “replace x by 3”)In general, given a system of linear equations in n unknowns, we will use operation I and III to try to obtain an equivalent system that is strictly triangular.We can associate with a linear system an mxn array of numbers whose entries are coefficient of theix ’s. we will refer to this array as thecoefficient matrix (系数矩阵) of the system.111212122212.....................n nm m m n a a a a a a a a a ⎛⎫⎪ ⎪ ⎪ ⎪⎝⎭A matrix （矩阵） is a rectangular array of numbersIf we attach to the coefficient matrix an additional column whose entries are the numbers on the right-hand side of the system, we obtain the new matrix11121121222212n n s m m m na a ab a a a b b a a a ⎛⎫ ⎪ ⎪ ⎪⎝⎭We refer to this new matrix as the augmented matrix （增广矩阵） of a linear system.The system can be solved by performing operations on the augmented matrix. i x ’s are placeholders that can be omitted until the endof computation.Corresponding to the three operations used to obtain equivalent systems, the following row operation may be applied to the augmented matrix.1.5 Elementary row operationsThere are three elementary row operations:(1)Interchange two rows;(2)Multiply a row by a nonzero number;(3)Replace a row by its sum with a multiple of another row.Remark: The importance of these three operations is that they do not change the solution set of a linear system and may reduce a linear system to a simpler form.An example is given here to illustrate how to perform row operations on a matrix.★Example:The procedure for applying the three elementary row operations:Step 1: Choose a pivot element (主元)(nonzero) from among the entries in the first column. The row containing the pivotnumber is called a pivotal row（主行）. We interchange therows (if necessary) so that the pivotal row is the new firstrow.Multiples of the pivotal row are then subtracted form each of the remaining n-1 rows so as to obtain 0’s in the firstentries of rows 2 through n.Step2: Choose a pivot element from the nonzero entries in column 2, rows 2 through n of the matrix. The row containing thepivot element is then interchanged with the second row ( ifnecessary) of the matrix and is used as the new pivotal row.Multiples of the pivotal row are then subtracted form eachof the remaining n-2 rows so as to eliminate all entries belowthe pivot element in the second column.Step 3: The same procedure is repeated for columns 3 through n-1.Note that at the second step, row 1 and column 1 remain unchanged, at the third step, the first two rows and first two columns remain unchanged, and so on.At each step, the overall dimensions of the system are effectively reduced by 1. (The number of equations and the number of unknowns all decrease by 1.)If the elimination process can be carried out as described, we will arrive at an equivalent strictly triangular system after n-1 steps.However, the procedure will break down if all possible choices for a pivot element are all zero. When this happens, the alternative is to reduce the system to certain special echelon form（梯形矩阵）. AssignmentStudents should be able to do all problems.Hand-in problems are: # 7--#11§2. Row Echelon FormNew words and phrases:Row echelon form 行阶梯形Reduced echelon form 简化阶梯形 Lead variable 首变量 Free variable 自由变量Gaussian elimination 高斯消元Gaussian-Jordan reduction. 高斯-若当消元 Overdetermined system 超定方程组 Underdetermined systemHomogeneous system 齐次方程组 Trivial solution 平凡解2.1 Examples and DefinitionIn this section, we discuss how to use elementary row operations to solve mxn systems.Use an example to illustrate the idea.★ Example : Example 1 on page 13. Consider a system represented by the augmented matrix111111110011220031001131112241⎛⎫ ⎪--- ⎪ ⎪-- ⎪- ⎪ ⎪⎝⎭ 111111001120002253001131001130⎛⎫⎪ ⎪ ⎪ ⎪- ⎪ ⎪⎝⎭………..(The details will given in class)We see that at this stage the reduction to strict triangular form breaks down. Since our goal is to simplify the system as much as possible, we move over to the third column. From the example above, we see that the coefficient matrix that we end up with is not in strict triangular form,it is in staircase or echelon form (梯形矩阵).111111001120000013000004003⎛⎫ ⎪ ⎪ ⎪ ⎪- ⎪ ⎪-⎝⎭The equations represented by the last two rows are:12345345512=0 2=3 0=4 03x x x x x x x x x ++++=⎧⎪++⎪⎪⎨⎪-⎪=-⎪⎩Since there are no 5-tuples that could possibly satisfy these equations, the system is inconsistent.Change the system above to a consistent system.111111110011220031001133112244⎛⎫ ⎪--- ⎪ ⎪-- ⎪ ⎪ ⎪⎝⎭ 111111001120000013000000000⎛⎫⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭The last two equations of the reduced system will be satisfied for any 5-tuple. Thus the solution set will be the set of all 5-tuples satisfying the first 3 equations.The variables corresponding to the first nonzero element in each row of the augment matrix will be referred to as lead variable .（首变量） The remaining variables corresponding to the columns skipped in the reduction process will be referred to as free variables （自由变量）.If we transfer the free variables over to the right-hand side in the above system, then we obtain the system:1352435451 2 3x x x x x x x x x ++=--⎧⎪+=-⎨⎪=⎩which is strictly triangular in the unknown 1x 3x 5x . Thus for each pairof values assigned to 2xand4x , there will be a unique solution.★Definition: A matrix is said to be in row echelon form (i) If the first nonzero entry in each nonzero row is 1.(ii)If row k does not consist entirely of zeros, the number of leading zero entries in row k+1 is greater than the number of leading zero entries in row k.(iii) If there are rows whose entries are all zero, they are below therows having nonzero entries.★Definition : The process of using row operations I, II and III to transform a linear system into one whose augmented matrix is in row echelon form is called Gaussian elimination （高斯消元法）.Note that row operation II is necessary in order to scale the rows so that the lead coefficients are all 1.It is clear that if the row echelon form of the augmented matrix contains a row of the form (), the system is inconsistent.000|1Otherwise, the system will be consistent.If the system is consistent and the nonzero rows of the row echelon form of the matrix form a strictly triangular system (the number of nonzero rows<the number of unknowns), the system will have a unique solution. If the number of nonzero rows<the number of unknowns, then the system has infinitely many solutions. (There must be at least one free variable. We can assign the free variables arbitrary values and solve for the lead variables.)2.2 Overdetermined SystemsA linear system is said to be overdetermined if there are more equations than unknowns.2.3 Underdetermined SystemsA system of m linear equations in n unknowns is said to be underdetermined if there are fewer equations than unknowns (m<n). It is impossible for an underdetermined system to have only one solution.In the case where the row echelon form of a consistent system has free variables, it is convenient to continue the elimination process until all the entries above each lead 1 have been eliminated. The resulting reduced matrix is said to be in reduced row echelon form. For instance,111111001120000013000000000⎛⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭ 110004001106000013000000000⎛⎫⎪- ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭Put the free variables on the right-hand side, it follows that12345463x x x x x =-=--=Thus for any real numbersαandβ, the 5-tuple()463ααββ---is a solution.Thus all ordered 5-tuple of the form ()463ααββ--- aresolutions to the system.2.4 Reduced Row Echelon Form★Definition : A matrix is said to be in reduced row echelon form if :(i)the matrix is in row echelon form.(ii) The first nonzero entry in each row is the only nonzero entry in its column.The process of using elementary row operations to transform a matrix into reduced echelon form is called Gaussian-Jordan reduction.The procedure for solving a linear system:(i) Write down the augmented matrix associated to the system; (ii) Perform elementary row operations to reduce the augmented matrix into a row echelon form;(iii) If the system if consistent, reduce the row echelon form into areduced row echelon form. (iv) Write the solution in an n-tuple formRemark: Make sure that the students know the difference between the row echelon form and the reduced echelon form.Example 6 on page 18: Use Gauss-Jordan reduction to solve the system:1234123412343030220x x x x x x x x x x x x -+-+=⎧⎪+--=⎨⎪---=⎩The details of the solution will be given in class.2.5 Homogeneous SystemsA system of linear equations is said to be homogeneous if theconstants on the right-hand side are all zero.Homogeneous systems are always consistent since it has a trivial solution. If a homogeneous system has a unique solution, it must be the trivial solution.In the case that m<n (an underdetermined system), there will always free variables and, consequently, additional nontrivial solution.Theorem 1.2.1 An mxn homogeneous system of linear equations has a nontrivial solution if m<n.Proof A homogeneous system is always consistent. The row echelon form of the augmented matrix can have at most m nonzero rows. Thus there are at most m lead variables. There must be some free variable. The free variables can be assigned arbitrary values. For each assignment of values to the free variables, there is a solution to the system.AssignmentStudents should be able to do all problems except 17, 18, 20.Hand-in problems are 9, 10, 16,Select one problem from 14 and 19.§3. Matrix AlgebraNew words and phrases:Algebra 代数Scalar 数量，标量Scalar multiplication 数乘 Real number 实数 Complex number 复数 V ector 向量Row vector 行向量 Column vector 列向量Euclidean n-space n 维欧氏空间 Linear combination 线性组合 Zero matrix 零矩阵Identity matrix 单位矩阵 Diagonal matrix 对角矩阵 Triangular matrix 三角矩阵Upper triangular matrix 上三角矩阵 Lower triangular matrix 下三角矩阵 Transpose of a matrix 矩阵的转置(Multiplicative ) Inverse of a matrix 矩阵的逆 Singular matrix 奇异矩阵 Singularity 奇异性Nonsingular matrix 非奇异矩阵 Nonsingularity 非奇异性The term scalar (标量，数量) is referred to as a real number (实数) or a complex number （复数）. Matrix notationAn mxn matrix, a rectangular array of mn numbers.111212122212.....................n nm m m n a a a a a a a a a ⎛⎫⎪ ⎪ ⎪ ⎪⎝⎭()ij A a =3.1 VectorsMatrices that have only one row or one column are of special interest since they are used to represent solutions to linear systems.We will refer to an ordered n-tuple of real numbers as a vector （向量）.If an n-tuple is represented in terms of a 1xn matrix, then we will refer to it as a row vector . Alternatively, if the n-tuple is represented by an nx1 matrix, then we will refer to it as a column vector . In this course, we represent a vector as a column vector.The set of all nx1 matrices of real number is called Euclidean n-space (n 维欧氏空间) and is usually denoted by nR.Given a mxn matrix A, it is often necessary to refer to a particular row or column. The matrix A can be represented in terms of either its column vectors or its row vectors.12(a ,a ,,a )n A = ora (1,:)a(2,:)a(,:)A m ⎛⎫ ⎪⎪= ⎪ ⎪⎝⎭3.2 EqualityFor two matrices to be equal, they must have the same dimensions and their corresponding entries must agree★Definition : Two mxn matrices A and B are said to be equal ifij ij a b =for each ordered pair (i, j)3.3 Scalar MultiplicationIf A is a matrix,αis a scalar, thenαA is the mxn matrix formed by multiplying each of the entries of A byα.★Definition : If A is an mxn matrix, αis a scalar, thenαA is themxn matrix whose (i, j) is ij a αfor each ordered pair (i, j) .3.4 Matrix AdditionTwo matrices with the same dimensions can be added by adding their corresponding entries.★Definition : If A and B are both mxn matrices, then the sum A+B is the mxn matrix whose (i,j) entry isij ija b + for each ordered pair (i, j).An mxn zero matrix (零矩阵) is a matrix whose entries are all zero. It acts as an additive identity on the set of all mxn matrices.A+O=O+A=AThe additive of A is (-1)A since A+(-1)A=O=(-1)A+A.A-B=A+(-1)B-A=(-1)A3.5 Matrix Multiplication and Linear Systems3.5.1 MotivationsRepresent a linear system as a matrix equationWe have yet to defined the most important operation, the multiplications of two matrices. A 1x1 system can be writtena xb =A scalar can be treated as a 1x1 matrix. Our goal is to generalize the equation above so that we can represent an mxn system by a single equation.A X B=Case 1: 1xn systems 1122... n n a x a x a x b +++=If we set()12n A a a a =and12n x x X x ⎛⎫ ⎪⎪= ⎪ ⎪⎝⎭, and define1122...n n AX a x a x a x =+++Then the equation can be written as A X b =。
线性代数 英文讲义
Chapter 4 Linear Transformations In this chapter, we introduce the general concept of linear transformation from a vector space into a vector space. But, we mainly focus on linear transformations from n R to m R.§1 Definition and ExamplesNew words and phrasesMapping 映射Linear transformation 线性变换Linear operator 线性算子Dilation 扩张Contraction 收缩Projection 投影Reflection 反射Counterclockwise direction 反时针方向Clockwise direction 顺时针方向Image 像Kernel 核1.1 Definition★Definition A mapping(映射) L: V W is a rule that produces a correspondence between two sets of elements such that to each element in the first set there corresponds one and only one element in the second set.★Definition A mapping L from a vector space V into a vector space W is said to be a linear transformation（线性变换）if(1) 11221122(v v )(v )(v )L L L αααα+=+for all 12v ,v V ∈ and for all scalars 1α and 2α. (1) is equivalent to(2) 1212(v v )(v )(v )L L L +=+ for any 12v ,v V ∈ and(3) (v)(v)L L αα= for any v V ∈ and scalar α.Notation: A mapping L from a vector space V into a vector space W is denotedL: V →WWhen W and V are the same vector space, we will refer to a linear transformation L: V →V as a linear operator on V . Thus a linear operator is a linear transformation that maps a vector space V into itself.1.2 Linear Operators on 2R1. Dilations(扩张) and Contractions Let L be the operator defined byL(x)=k xthen this is a linear operator. If k is a positive scalar, then the linear operator can be thought of as a stretching or shrinking by a factor of k.120(x)x 0x k L A x k ⎛⎫⎛⎫== ⎪ ⎪⎝⎭⎝⎭2. Projection （投影）onto the coordinate axes.L(x)=11e x 1210(x)x 00x L A x ⎛⎫⎛⎫== ⎪⎪⎝⎭⎝⎭ L(x)=22e x 1200(x)x 01x L A x ⎛⎫⎛⎫== ⎪⎪⎝⎭⎝⎭3. Reflections (反射) about an axis Let L be the operator defined byL(x)=12(,)T x x -, then it is a linear operator. The operator L has theeffect of reflecting vectors about the x-axis. 1210(x)x 01x L A x ⎛⎫⎛⎫== ⎪ ⎪-⎝⎭⎝⎭Reflecting about the y-axis L(x)=12(,)T x x -, 1210(x)x 01x L A x -⎛⎫⎛⎫== ⎪ ⎪⎝⎭⎝⎭4. RotationsL(x)=21(,)T x x -, L has the effect of rotating each vector by 90 degrees in the counterclockwise direction （逆时针方向）.1201(x)x 10x L A x -⎛⎫⎛⎫== ⎪ ⎪⎝⎭⎝⎭1.3 Linear Transformations from n R to m RIf A is an mxn matrix, then we can define a linear transformation A L from n R to m R by()A L X AX =It is easy to verify that the mapping above is linear. In the next section, we will see that any linear transformation from n R to m R must be of this form.1.4 The Image and Kernel★Definition Let L: n R →m R is a linear transformation. The kernel （核）of L denoted ker(L), is defined by ker(L)={}v |(v)0W V L ∈=★Definition Let L: n R →m R is a linear transformation and let S be a subspace of V . The image （像）of S, denoted L(S), is defined by L(S)= {}w |w (v) for some v m n R L R ∈=∈The image of the entire vector space, L(V), is called the range （值域）of L.Theorem 4.1.1 If L: n R →m R is a linear transformation and S is a subspace of n R , then (i) ker(L) is a subspace of n R . (ii) L(S) is a subspace of m R .Assignment for section 1, chapter 4Hand in: 3, 4, 17, 20,Not required : 8, 10, 11, 15, 16, 19, 25§2 Matrix Representations of Linear TransformationsNew words and phrasesMatrix representation 矩阵表示 Formal multiplication 形式乘法 Similarity 相似性2.1 Matrix Representation of Linear TransformationsIn section 1 of this chapter, the examples of linear transformations can be represented by matrices. In general, a linear transformation can be represented by a matrix.If we use the basis E=[12u ,u ,,u n ] for U and the basisF=[12v ,v ,,v m ] for V , and L: U → V .If u is a vector in U, then1122u u u u n n x x x =+++ (in U) |→ 1122L(u)v v v m m y y y =+++ (in V)The linear transformation L is determined by the change of the coordinate vectors:12n x x x ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭→12m y y y ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭Assume that1122(u )v v v j j j mj m L a a a =+++, j=1, 2, …, nFormally,12[(u ),(u ),,(u )]n L L L =12[v ,v ,,v ]m 111212122212n n m m mn a a a a a a a a a ⎛⎫ ⎪ ⎪⎪⎪⎝⎭Write 12[(u ),(u ),,(u )]n L L L as linear combinations of 12[v ,v ,,v ]m , then consequently, A is obtained.Then L(u) = 1122(u u u )n n L x x x +++ =12[v ,v ,,v ]m 12m y y y ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭(formal multiplication)1122L(u )L(u )L(u )n n x x x =+++=nj=1(u )j j x L ∑1212[L(u ),L(u ),,L(u )]n n x xx ⎛⎫ ⎪ ⎪= ⎪ ⎪⎝⎭(formal multiplication)==11(v )n mj ij i j i x a =∑∑=i=11()v m nij j i j a x =∑∑=12[v ,v ,,v ]m 111212122212n n m m mn a a a a a a a a a ⎛⎫ ⎪ ⎪ ⎪⎪⎝⎭12n x x x ⎛⎫ ⎪ ⎪⎪ ⎪⎝⎭Hence12m y y y ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭=111212122212n n m m mn a a a aa a a a a ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭12n x x x ⎛⎫ ⎪ ⎪⎪ ⎪⎝⎭Thus, y=A x is the coordinate vector of L (u) with respect toF =[12v ,v ,,v m ]. y=A x is called the matrix representation of thelinear transformation. A is called the matrix representing L relative to thebases E and F. A is determined by the following equations.12[(u ),(u ),,(u )]n L L L =12[v ,v ,,v ]m 111212122212n n m m mn a a a a a a a a a ⎛⎫ ⎪ ⎪⎪⎪⎝⎭We have established the following theorem. Theorem 4.2.2 If E=[12u ,u ,,u n ] is an ordered basis for U andF=[12v ,v ,,v m ] is an ordered basis for V , then corresponding to eachlinear transformation L:U →V there is an mxn matrix A such that [()][]F E L u A u = for each u in U.A is the matrix representing L relative to the ordered bases E and F. In fact, a [(u )]j j F L =.2.2 Matrix Representation of L: n R →m RIf U=n R , V=m R , then we have the following theorem.Theorem 4.2.1 If L is a linear transformation mapping n R into m R , there is an mxn matrix A such thatL (x)=A xfor each x n R ∈. In fact, the jth column vector of A is given by12((e ),(e ),,(e ))n A L L L =Proof If we choose standard basis 12[e ,e ,,e ]n for n R and thestandard basis 12[e ,e ,,e ]m for m R ,L(x)= 1122(e e e )n n L x x x +++=12(e ,e ,,e )m 12m y y y ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭=12m y y y ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭1122L(e )L(e )L(e )n n x x x =+++=nj=1(e )j j x L ∑1212(L(e ),L(e ),,L(e ))n n x x x ⎛⎫ ⎪ ⎪= ⎪ ⎪⎝⎭And let A=()ij a =()12a ,a ,,a n 12(L(e ),L(e ),,L(e ))n =If 1122x e e e n n x x x =+++, then L(x)=Ax.A is referred to as the standard matrix representation (标准矩阵表示) of L.( A representation with respect to the standard basis.)Example 1 (example 1 on page 186) Determine the standard matrix representation of L.Define the linear transformation L:3R 2R by1223(x)(,)T L x x x x =++ for each 123x (,,)T x x x = in 3R , find the linear standard representation of L.Solution: Find 123L(e ),L(e ),L(e ). Then 123110(L(e ),L(e ),L(e ))011A ⎛⎫== ⎪⎝⎭Example 2 rotation by an angle θLet L be the linear transformation operator on 2R that rotates each vector by an angle θ in the counterclockwise direction. We can see that1e is mapped to (cos ,sin )T θθ, and 2e is mapped to (sin ,cos )T θθ-.1(e )(cos ,sin )T L θθ=, 2(e )(sin ,cos )T L θθ=-The matrix A representing the transformation will be12cos sin (L(e ),L(e ))sin cos A θθθθ-⎛⎫==⎪⎝⎭To find the matrix representation A for a linear transformation L n R→ m R w.r.t. the bases E=[12u ,u ,,u n ] and F=[12b ,b ,,b m ], wemust represent each vector 1122(u )b b b j j j mj m L a a a =+++. The followingtheorem shows that determining this representation is equivalent to solving the linear system Bx=(u )j L , where (u )j L is regarded as a column vector in m R .Theorem 4.2.3 Let E =[12u ,u ,,u n ] and F =[12b ,b ,,b m ] beordered bases for n R and m R , respectively. If L : n R → m R is a linear transformation and A is the matrix representing L with respect to E and F , then112((u ),(u ),,(u ))n A B L L L -=where B =(12b ,b ,,b m ).Proof L(u) = 1122(u u u )n n L x x x +++ =12(b ,b ,,b )m 12m y y y ⎛⎫⎪ ⎪ ⎪ ⎪⎝⎭1122L(u )L(u )L(u )n n x x x =+++=nj=1(u )j j x L ∑1212(L(u ),L(u ),,L(u ))n n x xx ⎛⎫ ⎪ ⎪= ⎪ ⎪⎝⎭12(b ,b ,,b )m 12m y y y ⎛⎫ ⎪ ⎪ ⎪ ⎪⎝⎭1212(L(u ),L(u ),,L(u ))n n x x x ⎛⎫ ⎪ ⎪= ⎪ ⎪⎝⎭The matrix B is nonsingular since its column vectors form a basis form R . Hence, 112((u ),(u ),,(u ))n A B L L L -=12((u ),(u ),,(u ))n L L L is the matrix representing L relative to the bases [12u ,u ,,u n ] and [12e ,e ,,e m ]. B is the transition matrixcorresponding to the change of basis from [12b ,b ,,b m ] to[12e ,e ,,e m ].Corollary 4.2.4 If A is the matrix representing the linear transformation L:n R m R with respect to the bases12m [b ,b ,,b ]1B -12m [e ,e ,,e ]12n [u ,u ,,u ] A12((),(),,())n L u L u L uBE=[12u ,u ,,u n ] and F=[12b ,b ,,b m ]then the reduced row echelon form of1212(b ,b ,,b |(u ),L(u ),,L(u ))m n Lis (I |A )Proof 1212(b ,b ,,b |(u ),L(u ),,L(u ))m n L =(B|BA), which is rowequivalent to (I|A).Examples Finding the matrix representing L Example 3 on page 188Let L be a linear transformation mapping 3R into 2R defined by 11232L(x)b ()b x x x =++. Find the matrix A representing L with respect to the ordered bases 123[e ,e ,e ] and 12[b ,b ], where 11b 1⎛⎫= ⎪⎝⎭, 21b 1-⎛⎫= ⎪⎝⎭Solution:Method 1. Represent 123[e ,e ,e ] in terms of 12[b ,b ] Method 2. 112123(b ,b )((e ),(e ),(e ))A L L L -=1111111/21/2111100111111/21/2111011A ------⎛⎫⎛⎫⎛⎫⎛⎫⎛⎫=== ⎪ ⎪ ⎪⎪ ⎪-⎝⎭⎝⎭⎝⎭⎝⎭⎝⎭Method 3 Applying row operations. 12123(b ,b |(e ),(e ),(e ))L L L Example 4 on page 188Let L be a linear transformation mapping 2R into itself defined by 1212L(b b )()b 2b αβαββ+=++, where 12[b ,b ] is the ordered basisdefined in example 3. Find the matrix A representing L with respect to12[b ,b ].Solution: Use three methods as in example 3. Example 6 on page 190Determine the matrix representation of L with respect to the given bases. Let L: 2R 3R be the linear transformation defined by 21212L(x)(,,)T x x x x x =+-Find the matrix representation of L with respect to the ordered bases12[u ,u ] and 123[b ,b ,b ], where12u (1,2),u (3,1)T T ==123b (1,0,0),b (1,1,0),b (1,1,1)T T T ===Assignment for section 2, chapter 4Hand in: 2, 6, 8, 16, 20 Not required: 9—15, 17, 19§3 SimilarityLet L be a linear operator on V , E=[12v ,v ,,v n ] be an orderedbasis for V , A is the matrix representing L with respect to the basis E. 1122u v v v n n x x x =+++, 1122L(u)v v v n n y y y =+++1211221212(v )v v v [v ,v ,,v ][v ,v ,,v ]a j j j j j nj n n n j nj a a L a a a a ⎛⎫ ⎪ ⎪=+++== ⎪ ⎪ ⎪⎝⎭y=Ax F=[12w ,w ,,w n ]1122u w w w n n c c c =+++, 1122L(u)w w w n n d d d =+++1211221212(w )w w w [w ,w ,,w ][w ,w ,,w ]b j jj j j nj n n n j nj b b L b b b b ⎛⎫ ⎪ ⎪=+++== ⎪ ⎪ ⎪⎝⎭d=BcLet the transition matrix corresponding the change of basis from F=[12w ,w ,,w n ] to [12v ,v ,,v n ]Then x=Sc, y=Sd, 11y x S BS --= 1y x SBS -= or 1A SBS -=Hence, we have established the following theorem.Theorem 4.3.1 Let E=[12v ,v ,,v n ] and F=[12w ,w ,,w n ] betwo ordered bases for a vector space V , and let L be a linear operator onn R . Let S be the transition matrix representing the change from F to E. IfA is the matrix representing L with respect to E, andB is the matrix representing L with respect to F, then 1B S AS -=.★Definition Let A and B be nxn matrices. B is said to be similar to A if there is a nonsingular matrix S such that 1B S AS -=.Example 2 (on page 204)Example Let L be the linear operator on 3R defined by L(x)=Ax, whereV VV VBasis E=12n [v ,v ,,v ] Su →L(u)u →L(u)Ax=yBc=dS -1Coordinate vector of L(u): dBasis FCoordinate vector of L(u) :y Basis ECoordinate vector of u: xCoordinate vector of u: c Basis E=12n [w ,w ,,w ] x=Sc y=Sd220112112⎛⎫ ⎪ ⎪ ⎪⎝⎭. Thus the matrix A represents L with respect to the standard basis for 3R . Find the matrix representing L with respect to the basis [123y ,y ,y ], where 1y (1,1,0)T =-, 2y (2,1,1)T =-, 3y (1,1,1)T =. SolutionD=000010004⎛⎫⎪⎪ ⎪⎝⎭is the matrix representing L w.r.t the basis [123y ,y ,y ],. Or, we can find D using 1D Y AY -= 11x ()x=()x n n n A YDY YD Y --=Using this example to show that it is desirable to find as simple as a representation as possible for a linear operator. In particular, if the operator can be represented by a diagonal matrix, this is usually preferred representation. It makes the computation of Dx and x n D easier.Assignment for section 3, chapter 4Hand in: 2, 3, 4, 8, 10, 15 Not required 5, 6。
《大学英语一》期终考试试卷(A卷)及答案
适用专业：注意：答案必须写在答题纸上，否则按零分计。
Part ⅠListening Comprehension (15%) (15 minutes)Direction: This part is to test your listening ability. It consists of 3 sections.Section ADirections:This section is to test your ability to give proper responses. There are 5 recorded questions in it. After each question, there is a pause. The questions will be spoken two times. When you hear a question, you should decide on the correct answer from the 4 choices marked A), B), C) and D) given in your test paper. Then you should mark the corresponding letter on the Answer Sheet with a single line through the center.Example: You will hear:You will read: A) I’m not sure. B) You’re right.C) Y es, certainly. D) That’s interesting.From the question we learn that the speaker is asking the listener to leave a message. Therefore, C) Yes, certainly is the correct answer. You should mark C) on the Answer Sheet. Now the test will begin.1. A) That’s all right.. B) It is a pleasant day.C) I’d love to. D) This football player is famous.2. A) Could I have 2 kilos? B) It’s five yuan a kilo.C)It is too expensive. D) It’s three kilos.3. A) I do my homework at seven in the evening. B) I was drawing an elephant.C) I will go shopping. D) I’m watching TV in the room..4. A) That’s all right. B) You’d better put it under the tree.C) Don’t put it here. D) It is brand-new.5. A)Twice a week. B) Four times a week.C)Twenty-five minutes. D) Bus No. 1 will take you there.Section BDirections:This section is to test your ability to understand short dialogues. There are 5 recorded dialogues in it. After each dialogue, there is a recorded question. Both the dialogues and questions will be spoken two times. When you hear a question, you should decide on the correct answer from the 4 choices marked A), B), C) and D) given in your test paper. Then you should markthe corresponding letter on the Answer Sheet with a single line through the center.6. A) January. B) February.C) March. D) April.7. A) Warm. B) Cool.C) Cold. D) Hot.8. A) Because the colour of the dress is not her liking.B) Because the size of the dress is not big enough.C) Because the price of the dress is too high.D) Because she borrowed the dress.9. A) She suggests the man should not look at the advertisements.B) She suggests nothing.C) She means that the advertisements are of no use.D) She suggests the man should look at the advertisement.10. A) Whether the man is good at EnglishB) Whether the woman has passed the examination.C) Whether the woman is about to have an English examination.D) Whether the woman is preparing for the English examinationSection CDirections: In this section you will hear a recorded short passage. The passage is printed in the test paper, but with some words or phrases missing. The passage will be read three times. During the second reading, you are required to put the missing words or phrases on the Answer Sheet in order of the numbered blanks according to what you hear. The third reading is for you to check your writing. Now the passage will begin.Color blindness is another eye defect(疾病) that many people have. People who are color blind cannot __11________the difference between certain colors. Most color blind people can only see two____12__colors of the rainbow and confuse other colors. Very few people are completely color people. 13 other eye defects, color blindness cannot be cured. Although we can’t cure many eye defects, we can 14 our eyes. People are always saying that carrots are good for our eyes. This is because carrots help our 15 make Vitamin A(维生素A) which helps our eyes work. People often joke by saying that this is why rabbits don’t wear glasses.Part II. Vocabulary & StructureDirections: This part is to test your ability to use words and phrases correctly. It consists of 2 sections.Section A (15%)Directions:In this section, there are 15 incomplete sentences. You are required to complete each statement by choosing the appropriate answer form the 4 choices marked A), B), C) and C). You should mark the corresponding letter on the Answer Sheet with a single line through the center.1.The family gathered together to ___________ the holiday meals.A) divide B) share C) receive D) smell2. Helen asked me __________ the film called “Star War.”A) have I seen B) had I seenC) whether I have seen D) if I had seen3. My parents are not used to_____ in big cities.A）live B）living C）have lived D）be living4. Women, _________ men, have the right to work.A) as soon as B）as long as C）as far as D）as well as5. It wasn’t as good a dinner_______ she had promised us.A) as B）that C）which D）what6. The prices of computers range _______4000 yuan to 6000 yuan.A) about B)with C）from D）up7. The shirt is ____for you to wear.A) too tighter B）too tight C) so tight D) much tighter8. She is twenty, so by law her father can’t__________ her marriage.A) force B) prevent C)separate D)fail9. We arrived at a farmhouse, in front of_______ sat a little boy.A) it B)that C) which D) what10. _______ so much progress in such a short period of time.A) Never have any country made B) Never have a country madeC) Never has any country made D) Never did a country made11. Finally, the thief got ________ by the policeman.A) pursued B) caught C) removed D) recovered12._____ is a fact that English is being accepted as an international language.A) There B) This C) That D) It13. She never laughed, _________ lose her temper.A) or she ever did B) nor did she everC）or did she ever D）nor she ever did14. It is vital that enough money ________ to fund the project.A) is collected B) be collectedC) must be collected D) can be collected15. No one had told Smith about_________ a lecture the following day.A) there being B) there be C）there would be D）there wasSection B (15%)Directions: There are 15 incomplete statements here. You should fill in each blank with the proper form of the word given in brackets. Write the word or words in the corresponding space on the Answer Sheet.1.People speak of Mark Twain as the most (fame) ______________ writer of all times.2.I proposed that UK copyrights for sound recordings (extend) _____________ to 95 years.3.The doctor asked the old man to give up (smoke) _______________ because of his bad health.4.He examined the letter as (care) _______________ as he could.5.Here is the letter from a foreign company (concern) _______________ the order of our newproducts.6.She went to the tailor’s and had her overcoat (short) _________________.7.(personal) ___________________, I think he is a very nice partner, though you may not agree.8.He is an (experience) ____________ salesman of our company.9.She forgot (turn off) ___________________the light last night; the light has been on all the night.10.It is no use (cry) _____________over the spilt milk.11.My suggestion is that we (take) ____________actions at once.12.It was (puzzle) ____________ why the patient didn’t respond to the treatment.13.She told us such (fun) ____________ stories about their holiday.14.The children stopped (talk) ____________as the teacher came in.15.We don’t doubt Jack’s (able) ______________ to do the work.Part III Reading Comprehension (40%)Task 1 (10%)Directions: Reading the following passages and choose the best answer for each of the questions.When you see Sally, she is usually carrying a book under her arm. I am not talking only about the times when you see her at school. She often has a book with her when she is shopping , riding in the car , going to see relatives, or doing just about anything where there might be an opportunity ( 机会) to read . Now , you might think Sally is a bookworm (书呆子) , but that would not be accurate because she also enjoys spending a lot of time with her friends and doing lots of different things . Very simply put , books are one of Sally’s main hobbies .People practice their hobbies in many different ways .Some people like to collect stamps , others like to listen to music or go to the movies , and still others like to travel and visit new places . Sally likes to read books --- many different kinds of books. When she finds a good book in the library , she usually borrows it to investigate (研究) more deeply . She also likes to go to a large bookstore near her home, where she can see all kinds of new books and sometimes buy one that she likes.Sally’s love of books has made it a lot easier for her to do well in school because, after all, you do have to read a lot of books in your classes. When Sally gets an assignment and has to read a chapter, it almost seems like she is practicing her hobby . The books she uses in her classes are written very clearly and are really quite interesting. The only different thing is that sometimes she has to do a written exercise for homework. To Sally that seems like a small price to pay for the opportunity to read another book about something new and interesting. As Sally has read so many books and learned so many new words, she usually only has to do an assigned reading once because she understands just about everything the first time through.1.What is Sally usually doing when you see her?A)She is shopping.B)She is riding in a car.C)She is carrying a book under her arm.D)She is reading in a classroom.2.Why is it not accurate to say that Sally is a bookworm?A)Because reading is just one of her hobbies.B)Because she practices her hobbies in very simple ways.C)Because books make her look like a student.D)Because she does everything better than other people.3.The writer talks about people’s different hobbies in the second paragraph in order to tellus________.A)how many hobbies there might be among different peopleB)that reading is something that everybody likes to doC)why Sally likes reading more than other hobbiesD)that reading is a healthier hobby than other hobbies4.Sally finds it easier for her to do well in school because __________.A)through reading she has learnt a lot alreadyB)the books she uses in her classes are interestingC)once she finishes a book , she never reads it againD)she pays a small price for the opportunity to read her books5. What does Sally not like to do according to the third paragraph?A) Fast reading. B) Reading assignments.C) Chapter questions. D) Written exercises.Task 2 (10%)Directions: Reading the following passages and choose the best answer for each of the questions.No matter how you look on paper, no matter how well you present yourself, no matter how well you answer their questions, you will not get the job unless you make a personal connection with the interviewer. I need to know from the very start that you are someone I can trust to represent my company and me. How do you establish that trust? Simple. At the very beginning of the interview, when the introductions are being made, concentrate on looking directly and solidly into the interviewers’ eyes, giving them your sweetest and most endearing smile. I tend to think of it as a “shy smile”. The bottom lin e is to make it a warm and friendly smile. Then think about the fact that you are truly pleased to be there in the presence of this person. Establish that personal connection both physically and mentally with the interviewer.How do you know when the connection is made? When they return your smile in a comfortable, relaxed manner, you are connected and ready to communicate on a personal level. Remember, I only hire people I am comfortable with. If the connection is not made, I won’t hire. So take the time t o establish that personal connection.6. Which of the following is the most important factor for you to get the job?A) To wear formally and tidily.B) To prepare a good paper and all the materials needed.C) To present myself as well as possible.D) To make a personal connection with the interviewer.7. Which of the following statements is TRUE?A) It is not necessary to make eye contact with the interviewer.B) If you want to be trusted, you should know much more information about the interviewer.C) If you want to get the job, you must make the interviewer trust you with personal connection.D) It is necessary to keep smiling during the interview.8. What’s the way about establishing the trust at the very beginning of the interview t he passage mentioned?A) To stare at the interviewers’ eyes straightly during the interview.B) To be a shy person and not to sit down unless being asked.C) To give the interviewer a warm and friendly smile.D) To be a polite person and try to persuade the interviewer with rich working experience.9. How do you know when the personal connection is made?A) When the interviewer asks the questions with a smile.B) When the interviewer smiles during the whole interview.C) When the interviewee smiles during the whole interview.D) When the interviewer returns the interviewee’s smile in a comfortable, relax manner.10.Which of the following would be the most proper title of the passage?A) How to Establish Personal Connection in an InterviewB) What You Should Do in an InterviewC) How an Interviewee Can Be HiredD) The Role of Personal CommunicationTask 3 (10%)Directions:Reading the following passages and choose the best answer for each of the questions.The entertainment profession, or “show business”, attracts many young people. Unfortunately, only very few can hope to become famous. Talent is not enough, because show business is as competitive as any other business. Without a good manager, a performer can never hope to succeed. Fashion is important in his business, too. The best tailor in the world will never be a success if he makes old-fashioned clothes. In exactly the same way, a performer must change his “act” in order to follow the taste of the moment. This is true for actors, dancers and comedians, but perhaps most of all for singers.“Pop” stands for “ popular”, and a pop singer has to work very hard to become popular. He must either give the public what they already want, or he must find a new way of singing that will attract their attention. Even when he has succeeded, and his records are sold everywhere, he cannot relax. Then he must work harder than ever to remain popular, because there are always younger singers trying to become famous and to steal some of the popularity.The life of a successful pop singer is not at all easy. He can only relax when he is alone, becauseeverything he does is watched and reported in the special newspaper written for the“fans”. The fans are the most important people in the world for the singer. They buy his records, they go to his concerts, and they make him rich and famous. But they can be very annoying, too. Sometimes they get so crazy that they do anything to get a “souvenir”. They steal handkerchiefs, they tear off buttons, and they even cut off pieces of the unfortunate singer’s hair.Many singers have been forced to hide, and some who have not been so lucky as to escape have been stripped practically naked by their fans. A pop singer has to spend a lot of money on clothes, because he must always look smart, or, at any rate, different. He must have a luxurious car. And most important he must always keep smiling for the benefit of his public.11. How many of the young can hope to become famous?A) Nobody. B) Only very few.C) The majority of them. D) All of them.12. Which of the following is the key element to become a successful performer?A) The age. B) Education background.C) A wealthy family. D) A good manager.13. Why must a pop singer work harder when he has become famous?A) To sell more records. B) To follow the taste of the moment.C) To stay popular. D) To attract the public’s attention.14. It may be inferred from this passage that_______ .A) a pop singer is afraid of meeting his fansB) some people become pop singers by chanceC) a pop singer sometimes is unwilling to meet peopleD) pop singers have to smile all the time15. A suitable title for this passage might be_______ .A) “The Entertainment Profession” B) “How to Become a Pop Singer”C) “A Pop Singer’s Life” D) “The Pop Singer”Task 4 (10%)Directions: Reading the following passages and choose the best answer for each of the questions.Dear Sir or Madam,The ABC Company was established in 2006 and in four short years has become one of the most successful companies in the market place. For this, we are pleased ,proud and grateful .We are pleased because our customers have confirmed our belief that if the products we offer are new, exciting, innovative and of excellent quality, they will be purchased.We are proud because we know we are a company that keeps its word to its customers; that guarantees that any product can be returned within 30 days if it proves to be unsatisfactory in any way; and that always lets our customers know if there is to be a delay in delivery.We are grateful to customers like you, because you confirm our beliefs that good service andquality result in satisfied customers. Without you, there would be no reason for us to be pleased or proud. We thank you for your orders and for giving us the opportunity to be of service to you.Our special summer catalogue is at the printers and should be in your home soon. We hope that you will be pleased with the new selections.Yours faithfullyJohn Brown16. From the passage we can learn that ABC Company always_______.A) keeps its promise B) provides the same productsC) sells its products at a low price D) delivers its products without delay17. ABC Company believes that its customers are satisfied because the company_____.A) gives them opportunities to order B) provides good service and qualityC) guarantees the quickest delivery D) sends new catalogues to them18.The customers will be informed if _______.A) the product can’t be delivered on timeB) the product is out-of-date and unsatisfactoryC) the company doesn’t accept the returned productD) the company can’t send a new catalogue on time19.The purpose of this letter s to___________.A) tell the customers about the quality of their productsB) express the company ‘s thanks to the customersC) prove the excellent service of the companyD) inform the customers of a new catalogue20.What can we learn about the company ?A) It has the largest number of customers.B) It is grateful for its employees’ efforts.C) It is successful in the market place.D) It charges the least for its services.Part V Translation (15%)Section A: choose the best answer (6%)1.They are developing new drugs for cancer.A)他们新发明的药可以致癌。
广东省东莞市英语初二上学期期中试卷与参考答案(2024年)
2024年广东省东莞市英语初二上学期期中自测试卷与参考答案一、听力部分（本大题有20小题，每小题1分，共20分）1、Listen to the first conversation.Conversation:M: Can I help you find your classroom, Alice?W: Yes, please. It’s my first day here.Question:1、What is Alice doing?A. She’s helping someone.B. She’s looking for her classroom.C. She’s in her classroom already.D. She’s greeting a new student.Answer: BExplanation:From the conversation, it is clear that Alice is new and needs help finding her classroom, indicating that she is looking for her classroom.2、Listen to the second conversation.Conversation:W: Did you finish your homework?M: Not yet, but I’m going to after dinner.Question:2、When will the boy finish his homework?A. Before dinner.B. During dinner.C. After dinner.D. He won’t f inish it.Answer: CExplanation: The boy explicitly states that he will do his homework after dinner, which makes option C the correct choice.3、Listen to the conversation between two students, Jack and Lily, discussing their weekend plans. After listening, answer the question.Question: What does Jack plan to do on Sunday afternoon?A. He will go to the library to study.B. He will go to a movie with his friends.C. He will visit his grandparents.Answer: CExplanation: In the conversation, Jack mentions that he is planning to visit his grandparents on Sunday afternoon, so the correct answer is C.4、Listen to a short dialogue between a teacher and a student about a homework assignment. After listening, answer the question.Question: What is the homework assignment for Monday?A. Write a short essay about their favorite book.B. Read a chapter from the science book and answer the questions at the end.C. Solve ten algebra problems and hand them in by Friday.Answer: BExplanation: The teacher tells the student that they need to read a chapter from the science book and answer the questions at the end. Therefore, the correct answer is B.5、Listen to the dialogue between two students talking about their school project. What subject are they planning their project around?A. HistoryB. ScienceC. GeographyCorrect Answer: B. ScienceExplanation: In the dialogue, one student mentions that they need to collect data for their science project by observing the growth of plants under different conditions. This indicates that their project is related to the field of science.6、In the recorded talk, the speaker discusses the importance of recycling in our daily lives. According to the speaker, which item is NOT mentioned as something that can be recycled?A. PaperB. GlassC. BatteriesCorrect Answer: C. BatteriesExplanation: The speaker lists several items that can be recycled, such as paper and glass, but does not mention batteries. Therefore, batteries are not part of the items discussed that can be recycled in the context of the talk.7、Listen to the conversation and choose the best answer to the question you hear.Question: What are the speakers discussing?A. A school eventB. A book they recently readC. Their weekend plansAnswer: AExplanation: The conversation starts with one speaker mentioning a school event, which is the main topic of their discussion.8、Listen to the short dialogue and fill in the blanks with the missing words you hear.Question: W: Hi, John. I heard you had a great time last weekend. What did you do?M: Well, I went to the___________with some friends. We had a lot of fun playing games and eating ___________.Answer: beach, ice creamExplanation: The dialogue mentions going to the beach, which is a common activity for relaxation and fun, and eating ice cream, which is a popular treat at thebeach.9、What does the boy want to do after school?A. Play basketballB. Go to the libraryC. Meet his friends at the parkAnswer: C. Meet his friends at the park.Explanation:In the dialogue, the boy mentions that he has finished all his homework and would like to meet up with his friends at the park to relax aftera busy week.10、How does the girl feel about the upcoming test?A. She feels confident because she has studied well.B. She feels nervous and unprepared.C. She feels indifferent as she believes the test is not important.Answer: A. She feels confident because she has studied well.Explanation:During the conversation, the girl expresses her readiness for the test, mentioning that she has been studying every day for the past week and feels very prepared.11.You are listening to a conversation between two students, Alice and Bob. They are discussing their weekend plans.Question: What does Alice decide to do for her weekend?A. Go to the movies.B. Visit her grandparents.C. Stay home and read books.D. Go hiking.Answer: BExplanation: In the conversation, Alice mentions that she wants to visit her grandparents in the countryside over the weekend. Therefore, the correct answer is B.12.You are listening to a short dialogue between a teacher and a student about a school project.Question: What is the teacher’s suggestion for improving the student’s project?A. Add more pictures.B. Write a longer introduction.C. Include more statistics.D. Change the project topic.Answer: CExplanation: In the dialogue, the teacher suggests that the student includes more statistics to make the project more informative and convincing. Hence, the correct answer is C.13、What does the boy plan to do on Saturday?A)Go to the libraryB)Visit his grandparentsC)Play basketball with friendsAnswer: C) Play basketball with friendsExplanation: In the conversation, the boy mentions that he’s going to play basketball with friends on Saturday. He says, “I’m hitting the court with my buddies this Saturday,” which indicates he plans to play basketball. The other options are not mentioned in the dialogue.14、Where is the conversation most likely taking place?A)At a restaurantB)In a classroomC)At a train stationAnswer: A) At a restaurantExplanation: The speakers discuss ordering food and the waiter bringing their meals, which suggests they are at a restaurant. Phrases such as “Can I take your order?” and “Here is your steak, medium-rare, just as you requested” provide clear context clues that the setting is a restaurant. The other locations are not supported by the content of the conversation.15.You hear a conversation between two students, Alice and Bob, discussing their weekend plans.Alice: “Hey Bob, do you have any plans for the weekend?”Bob: “Not really, Alice. I was thinking of going hiking, but it’s been raining a lot lately.”Alice: “That’s a bummer. Maybe we can go to the museum instead.”Bob: “That sounds good. I’ve been wanting to see the new art exhibit there.”Alice: “Great! Let’s meet at the library at 10 a.m. on Saturday.”Question: What is Bob’s initial plan for the weekend?A) To go hikingB) To go to the museumC) To stay homeD) To go shoppingAnswer: A) To go hikingExplanation: Bob initially mentions that he was thinking of going hiking, which indicates his original plan.16.You hear a teacher, Mr. Smith, giving instructions to his class.Mr. Smith: “Good morning, class. I hope you all had a good weekend. Today, we will be working on our science project. Remember, your task is to create a model of the solar system and bring it to class next Friday. Make sure to include all the planets and their orbits. You can use any materials you like, but I recommend using cardboard and pa int for a more durable model. Also, don’t forget to label each planet with its name and distance from the sun.”Question: What is the main assignment for the class?A) To write a book reportB) To create a model of the solar systemC) To study for a math testD) To participate in a science fairAnswer: B) To create a model of the solar systemExplanation: Mr. Smith explicitly mentions that the students need to create a model of the solar system as their main assignment.17、What does the man suggest doing?A. Going to the moviesB. Having dinner at a restaurantC. Staying home and cookingD. Visiting friendsAnswer: B. Having dinner at a restaurantExplanation: In the dialogue, the man mentions that he heard good reviews about a new Italian place and suggests they try it out. This indicates his preference for having dinner at a restaurant.18、Why can’t the woman go with the man?A. She has to work lateB. She is not feeling wellC. She already has plansD. She doesn’t like the restaurantAnswer: A. She has to work lateExplanation: The woman tells the man that she would love to join but she cannot because she has to finish up a project that is due tomorrow, which means she has to work late.19.You are listening to a conversation between a student and a teacher ina classroom.Student: “Teacher, when is the next math test?”Teacher: “The math test is scheduled for the last week of this month. Make sureyou study hard.”Question: When is the next math test?A. The first week of this monthB. The second week of this monthC. The last week of this monthD. Next monthAnswer: CExplanation: The teacher clearly mentioned that the math test is scheduled for the last week of this month. Therefore, the correct answer is C.20.You are listening to a phone conversation between two friends.Friend 1: “Hey, do you have any idea what movie we should watch this weekend?”Friend 2: “How about we go see the new superhero movie? It’s supposed to be really exciting!”Question: What movie are the friends planning to watch this weekend?A. A horror movieB. A romantic movieC. A superhero movieD. A comedy movieAnswer: CExplanation: Friend 2 suggested going to see the new superhero movie, indicating that it is their plan for the weekend. Hence, the correct answer is C.二、阅读理解（30分）Title: The Magic of LibrariesIn the age of the internet and smartphones, it might seem like libraries have become obsolete. However, nothing could be further from the truth. Libraries continue to play a crucial role in our communities, offering access to a wealth of information and resources that might otherwise be out of reach for many people.The first thing you notice when entering a library is the smell of books—new ones with their fresh scent and old ones with their musty aroma. Each book has a story not only within its pages but also in its history, who owned it before, and how it came to rest on the shelf. Libraries are not just about books though; they house magazines, newspapers, audio books, films, music, and sometimes even art exhibitions or craft workshops.Libraries provide a space where people can learn new skills, study quietly, or attend lectures and workshops. Many libraries offer free Wi-Fi, making them a valuable resource for students and job seekers alike. In addition, librarians are trained to help patrons find the information they need, whether it’s for school projects or personal interests.Moreover, libraries promote literacy and reading for pleasure, which is essential for the development of critical thinking and creativity. They organize events such as story time for children, book clubs for adults, and reading challenges to encourage everyone to read more. Libraries also serve as communityhubs where people can meet others with similar interests and form connections that enrich their lives.In conclusion, while technology has changed how we access information, libraries remain relevant by adapting to these changes and continuing to fulfill their mission of providing knowledge and cultural enrichment to all members of society.Questions:1.What does the author suggest is one of the first things you notice upon entering a library?A) The quiet atmosphereB) The smell of booksC) The librariansD) The computers2.According to the passage, what service do libraries offer besides books?A) Cooking classesB) Free Wi-FiC) Gym facilitiesD) Medical consultations3.How do libraries contribute to the community according to the text?A) By providing a venue for sports eventsB) By organizing literacy and social eventsC) By offering legal adviceD) By selling books at discounted pricesAnswers:1.B) The smell of books2.B) Free Wi-Fi3.B) By organizing literacy and social eventsThis reading comprehension exercise aims to test students’ ability to extract key information from a given text and understand the main points presented.三、完型填空（15分）Passage:Last weekend, the school held a science fair to showcase the projects that students had been working on throughout the semester. The fair was a great success, with many parents and teachers coming to see the innovative ideas and experiments. The students were excited to present their work and answer questions from the visitors.One of the most impressive projects was a solar-powered car built by a group of eighth-grade students. They had spent several months designing and constructing the car. The car was small, but it was equipped with solar panels that could charge its battery during the day. Here are some of the key points they discussed during the presentation:1.The solar panels on the car are made of a special type of material that can convert sunlight into electricity.2.The car has a battery that stores the electricity generated by the solar panels.3.The car can travel at a speed of about 15 miles per hour on a sunny day.4.The students used a computer program to simulate the car’s performance and make adjustments to its design.5.They tested the car on different types of roads to ensure its stability and safety.Choose the best word for each blank from the options given below.The students’ hard work an d dedication paid off, and their solar-powered car (1)_________________to the public with great success.1.A) was welcomed2.B) was accepted3.C) was rejected4.D) was ignoredAnswer: A) was welcomed四、语法填空题（本大题有10小题，每小题1分，共10分）1、My favorite fruit is the_______(1)_______that grows in my hometown. It’s sweet and juicy.A. oneB. onesC. thoseD. this答案：A解析：此处需要填入一个不定代词来指代前文提到的“my favorite fruit”，表示泛指，所以用“one”。
assignment
1.2 Information, Messages, and SignalsLet's begin with a dictionary definition of information: ``Knowledge communicated or received concerning some fact or circumstance; news.'' The world is full of facts, some discovered, some remaining to be discovered. These become information when they are used in some way. This is the fundamental connection between information and communication: a fact only becomes useful as information when it is communicated. This communication is often to a person, but that is not necessary! For example, information on the temperature in a room is communicated to the furnace via a thermostat, with no human involvement. In addition to the term information, we will be discussing two different, but related concepts: signal and message. A signal is the actual entity (electrical, optical, mechanical, etc.) that is transmitted from sender to receiver. For example, birds send out mating signals, which are specific sound patterns they create. Similarly, human vocal cords send out audible signals such as speech. A message, on the other hand, is the knowledge that is transmitted. For example, in the case of the birds, the message might be ``It's mating season and I'm available.'' Whereas the signal is a specific sequence of sound waves, the message is the meaning conveyed by that sequence. Message and information are quite closely related, and in some (not all) situations may be used interchangeably ; the subtle difference between them will be discussed later in this chapter. The concept of a signal is quite distinct from both, however; a signal need not convey any knowledge or information. In the following section we will discuss some common examples of information systems to illustrate the differences betweeninformation, messages, and signals. We will also use these examples to begin explaining the differences between analog and digital forms of information, and take a first look at how information might be measured or quantified.1.3.1 The PhonographThe human voice is an example of what we might call a ``natural signal''; that is, a type of signal that occurs as part of our human existence, and that typically carries information of great interest. Many other types of sounds also fit this description. Because sound in general, and voices in particular, are so central to human interaction, and so personal to each individual, there has long been a strong desire to store and transmit sounds and voices. The physics of acoustics lends itself to simple storage devices, and the first practical storage device, the phonograph, was invented by Thomas Edison in 1877. Sound is essentially mechanical vibrations, transmitted in air, and capable of stimulating vibrations in materials on which the vibrating air impinges. This is the principle behind how a basic phonograph records sounds: a diaphragm, which vibrates when sound waves impinge on it, is connected to a stylus which can cut or emboss grooves in a solid material. As the stylus is moved over the recording material (originally tinfoil, then wax cylinders, and eventually vinyl), the vibration induced into it from the diaphragm (which in turn is responding to the vibrating air) produces a groove whose depth or displacement is proportional to theinstantaneous sound intensity. In this way, a physical, permanent record of the sound is etched into the recording medium.The same mechanism that records the sounds can be used to play them back. If a playback stylus is allowed to travel across the grooves in the recording, it vibrates according to the groove pattern. This, in turn, vibrates the diaphragm, which creates sound waves that can be heard. Some amplification may be necessary for the sound waves to be acceptably loud, but aside from that, the recording and playback processes are quite symmetrical.This system is simple and elegant; its operation is made obvious by looking at it. There are a few basic design parameters: a recording medium soft enough to be embossed by the stylus, a source of motion for the recording medium that is steady and of the proper speed so that each oscillation of the acoustic wavefront is faithfully recorded, and a mechanical linkage that interfaces the moving air to the stylus. Certainly, there is no high technology at work here. But in fact, this simple phonograph, as seen in Figure 1.1, contains all the components of any communications system:●an input transducer (the device that converts a physical signal from a source, in this case sound, to an electrical,electro magnetic, or mechanical signal more suitable for communicating): in this case, the vibrating diaphragm during recording;●a transmitter (the device that sends the transduced signal): in this case, the recording stylus;●a transmission channel (the physical medium on which the signal is carried): in this case, the wax cylinder or other recording medium;●a receiver (the device that recovers the transmitted signal from the channel): in this case, the playback stylus; and●an output transducer (the device that converts the received signal back into a useful physical quantity): in this case, the vibrating diaphragm during playback. You can see the arrangement of these basic elements at the top of Figure 1.1. This type of abstract representation is known as a block diagram, and it is a very useful tool for representing complex systems . Each block represents a subsystem, whichperforms some function; the specific function determines the relationship between the signal entering the block and the signal leaving the block. The signals themselves are represented by arrows. Notice that the block diagram allows us to represent subsystems conceptually, without the need to worry about the actual physical components that make up each subsystem . This particular block diagram provides a model for many different communications systems; we have shown how it can be used to represent a phonograph and a satellite TV system.Note that in many of the communication systems with which you are familiar (telephone, radio, television), the transmission channel conveys the signal to the receiver immediately. However, systems such as this in which signals are stored for future user also considered communication systems, because they can be used to convey information from some source to a destination. Whether the source and destination are separated by space, time, or both, the system still conveys communication between these two parties.Figure 1.2:Zenith, 1951 vintage, combination Phonograph and Radio (from the collection of John C. Pelham).Within this system, we can also see examples of the quantities that we discussedearlier:●Signals: the original sound waves, the mechanical vibration of the recording stylus, the pattern on the wax cylinder, the mechanical vibration of the playback stylus, and the recreated sound waves are all signals.●Message: the content of the recording is the message, whether a song, a speech, or some other recorded sound.●Information: whatever the content of the recording conveys to the listener constitutes the information.This gives us a chance to discuss when message and information may be different. Information, in the context of this book, refers to conveyed knowledge that is in some way useful and not known previously. A message may contain a great deal of information (for example, a new song from your favorite recording artist), or it may contain very little (for example,a single note played over and over again). Although the basic phonograph (see Figure 1.2) constituted a breakthrough in the communication of information, it contained some significant limitations. If you have ever listened to a vintage recording on an old phonograph, you have heard evidence of these shortcomings. Desire for the reduction of these limitations has led us to the compact disc (CD) as the common commercial sound storage and playback medium today. In later chapters, we will not only discuss how CD technology works, but will provide explanations for why it does a better job of reproducing sound than did the basic phonograph.Try These Exercises1. List as many different forms of information relevant to your intended major area of study or profession as you can. If you are undecided concerning your profession, then choose something that you are considering. something that you are considering.2. In Section 1.3.1, the phonograph was analyzed as a communication system by identifying the following five components: the input transducer, the transmitter, the transmission channel, the receiver, and the output transmitter. Identify the same five components for each of the following communication systems. If you are not sure how something works, you might want to do some research in a library or on the Web.(a) Broadcast radio(b) A doorbell(c) Cable TV3. For each of the three communication systems listed in exercise 2, identify the following as best you can(a) Any signals used in the system(b) The message(c) The information contained in the message4. List two examples (other than those used in the text)of commonly encountered information that are analog. Then, list two examples that are digital. Finally, list two examples that are hybrids (i.e., contain both discrete and continuous aspects). For these, indicate which aspect is continuous, and which is discrete.5. List as many information systems as you can (at least four) that are found in yourhome or residence, and identify, as best you can, whether these systems are analog, digital, or both. Briefly explain the analog and/or digital aspects.6. Identify one new type of information system which has either been proposed, or is just appearing for sale or use. Describe this system in terms of the aspects discussed in this chapter (i.e., is it analog or digital, what is the bandwidth or data rate, etc.). Describe the new aspects of this system, compared to any previously existing systems which are similar.。
生物统计作业1
ClassNameI .D. No.Marks
Assignment 1 for Biostatistics (04110071)
Due date: Mar.12, 2013 1. (2 points each) Judge the statement (true or false) and explain why if you think it is false. (1).In a pie chart, the area of a given sector is the number or proportional to the percentage of individuals falling into that category. Judge: F Explain: In a pie chart, the area of a given sector is proportional to the percentage of individuals falling into that category. (2).The geometric mean is always less than the arithmetic mean if the data skewed to the right. Judge: T Explain: (3).The standard deviation may be regarded as an average of the deviations of the observations from the arithmetic mean. Judge: T Explain: (4).The mode often has a same value as the arithmetic mean and the median. Judge: F Explain: The mode often has a different value from both the arithmetic mean and the median. (5).Highly accurate data will always bring high level of precision. Judge: T Explain: (6).The arithmetic mean, geometric mean or varianceall can be used as measurements of the centraltendencyof data. Judge: F Explain: Variance is used to measure the degree of datadispersion. (7).An extreme value of the observation must be an outlier. Judge: F Explain: An extreme value sometimes is extreme results of variables inherent random variability, may be not an outlier. (8).Statistical diagrams, such as bar charts, histograms, and dynamic curve, can be used to show basic characters and changing patterns of any data collected. Judge: F Explain: The bar chart is useful for categorical or discrete data; thehistogram is useful for continuous data. (9).There must be a median existed in a data set. Judge: F Explain: If the number of data set observations is even, then the median lies midway between the central two observations. (10).A systematic error is one in which the recorded value is consistently above (or below) its true value, so we can say human error is systematic error. Judge:F Explain:human error is random error. 2. (2 points each) Please judge whether the following kinds of chart is an appropriate diagram to show the frequency distribution of a discrete variable (true or false), and explain why if you think
4-3大学英语4听力答案
4-3大学英语4听力答案Unit 3Part A1. W: Since it's the rush hour, lets take the subway.M: OK. Ifs not as direct as the bus, but ifs faster and there will be less chance of a traffic jam.Q: Why do the man and woman decide to take the subway?(C)2. M: I thought you said that Bob went to Sebring High School. W: No, he used to attend Clark High School, but after graduation last year. He enrolled in Melrose Community College where he is presently studying.Q: Where does Bob go to school now? (C)3. W: I hear that your son's working part time at the department store.M: Yes. He works Monday, Wednesday, and Friday from 3 to 7 and all day Saturday.Q: Which days does the man’s son not work? (C)4. M: Have you bought Jerry's birthday gifts yet?W: I've found the baseball shoes, a shirt, and a game, but not the bicycle.Q: Which of the following items has the woman not bought?(A)5. M: I still have to buy those tickets for tomorrow's concert.W: They may be gone by now. They've been on sale for a week and the singer is very popular.Q: What do we learn from this conversation? (A)6. M: Could you please explain the assignment for Monday, Miss Smith?W: Certainly, read the next chapter in your textbook and come to class prepared to discuss what you've read.Q: What is the probable relationship between the two speakers?(C)7. M: Do you think your grandfather heard our plans for the surprise party?W: No. He's partially deaf.Q: Why does the woman think the grandfather doesn't know about the party? (B)8. W: Louise speaks English as if she were an American.M: Her family lived in the United States until Louise was 12 years old. She has never forgotten her English.Q: Why can Louise speak English well? (D)9. W: Your library books are due on December thirteenth. If you haven't finished using them by then, you may renew them once. M: Thank you very much. I only need them for a few days.Q: When must the man return his books to the library? (D)10. M: Operator, we've been cut off. Would you please help me get my party again?W: I’ll try to connect you again with that area code.Q: What is the man's problem? (D)Part BPassage I Questions 11 to 13 are based on the following conversation:M: Do you have your television repaired?W: Yes, but not by the place you recommended.M: Why not? The repairmen are very good and the charges are so reasonable.W: That may be, but I couldn't find it.M: But you couldn't miss it. I told you the first right after the rail road bridge.W: I took that. I went to the end of the road. There is no such place.M: Wait a minute. Perhaps it is the second right. Yes, I think it is. W: I should have known. Whenever someone says "You can't miss it", you can be sure that you won't find it.11. What happened to the woman's television set? (A)12. Why couldn't the woman find the repair shop? (C)13. Why did the man recommend these television repairmen?(B)Passage IIQuestions 14 to 16 are based on the following passage: Jack was young, rich and fond of girls. He hardly ever did any work, and spent most of his time enjoying himself.One summer he bought a big motor boat. As soon as it was ready to go to sea, he telephoned to one of the girls he had met somewhere, and invited her for a trip in his new motor boat. It was the beginning of many successful invitations of this kind.The way Jack used to invite a girl for a trip in his boat was like this: he would begin by saying, "Hello, Laura (or whatever the girl's name was), I have just bought a beautiful new motor-boat, and I would like to take you out for a trip in it."The girl's answer was usually cautious, because everybody in that part of the country knew Jack's reputation with girls. She would say something like this: "Oh, really? That's nice. What name have you given to the boat?"Jack would then answer, "Well, Laura, I have named it after you.”Of course, the girl would feel very proud that Jack hadchosen her name for the boat out of the names of all his many girl-friends, and she would think that Jack must really love her. She would therefore be quite willing to accept his invitation to go for a trip in his motor-boat.It would not be until she got down to the harbor and actually saw the boat that she would understand how cleverly Jack had tricked her. Because there in neat gold letters on the boat she would see its name — "After You."14. What’s the name of the new motor boat? (B)15. Which of the following statements is true? (C)16. When would the girl feel very proud? (C)Passage IIIQuestions 17 to 20 are based on the following passage: In the early 1800's a new kind of power changed transportation and trade along the Mississippi River. This power was steam. People already knew how to use steam engines to run machines. Some people wanted to move boats in the same way. The first steamboat to travel on the Mississippi was the "New Orleans. " It made its first trip in 1811. It was a great success, and by 1819 there were 191 steamboats traveling on the river.In the past the farmers whose products went to other parts of the country used the steamboats. The manufacturers whose trade depended on cheap and easy transportation used the steamboats, too. Today many tourists come to travel on steamboats.17. What was the new kind of power in the early 1800’s? (C)18. On what river did the steamboat "New Orleans" travel?(B)19. Today, who use steamboats? (C)20. How many steam-boats were traveling on the river by1819?(D)Part C Compound DictationLife gets noisier every day and very few people can be free from noise of some sort or another. It doesn't (S1) matter where you live —in the middle of a modem city, or a (S2) faraway village –the chances are that you'll be (S3) disturbed by jet aeroplanes, (S4) transistor radios, oil-powered engines, etc. We seem to be getting used to noise, too. Some people feel quite lonely without (S5) background music while they're working.(S6) Scientific tests have shown that total silence can be a very(S7) frightening experience for a human being. However, (S8) some people enjoy listening to pop music which is very loud, and this can do harm to their ears. The noise level in some discos is far above the usual safety level for heavy industrial areas.One recent report about noise and concentration has suggested that although a lot of people say that any noise disturbs their concentration,(S9) what really affects their ability to concentrate is a change in the level of noise. It goes on to say (S10) that a background noise which doesn't change too much, such as music, may even help people to concentrate.Part D Listening and SpeakingAfter Monica left the office, she hurried down to the parking garage where her car was parked. As she searched in her purse for her car keys, she suddenly remembered that she had forgotten to lock the files where secret and important reports were kept. She knew that if her boss Mr. Henry found out that she had not locked the files, she could be fired.She turned and hurried back inside, waited impatiently forthe lift, and was glad that the trip to the seventh floor went without delay.As she hurried down the now dimly lit hall toward the offices of The Henry Company, she noticed that there was a light in Mr. Henry's office."Strange," she thought to herself, "I'm sure I turned all the lights out."Then she saw it. A man's shadow fell briefly across the glass of the door of the office and the lights went out."Oh, no. " She murmured to herself, her heart rising in her throat. "It must be a thief. What shall I do?"。
第三版大学英语1Unit 1
中南财经政法大学武汉学院外语系《大学英语1》(专科)课程教案Teaching Plan for College English(Book1) Foreign Languages Department of Wuhan College,ZNUEL课程名称(Course Title)College English授课学时(Class Periods)6授课单元或章节(Unit/Chapter)Unit1Text Some Strategies for Learning English教学目的及要求(Objectives& Requirements)Students will be able to:1.grasp the main idea of Text(six strategies for learningEnglish)and structure of Text(opening---body---conclusion);2.master the key language points in Text and learn how to usethem in context;3.Master the skills of writing in this unit:illustrating the main ideapoint by point.;教学方法及方式(Methods&Means)Questions,explanation,analysis,sentence-making,oral practice and exercises教学重点或难点(Key&DifficultPoints)1.Key expressions—by no means,nevertheless,while,complain of/about,bound,according to,constant,concentrate on,in addition to, opportunity,handle,absorb,put…into practiceage---according to3.Structure---not only…but also,it’s true that…,but…4.suffixes–ment and–ion(also–ation,-ition,-sion)5.The organization of an expositive piece of writing教学进程或步骤(Procedures orSteps)1.Warm-up questions and group discussions;2.Global reading:text organization,main information;3.Detailed reading:difficult sentences,language study;4.Post reading:useful expressions,reflections on the text;5.Check on homework;6.Further study and practice;教学内容(Contents)1.Topic-related questions&discussion:;ⅠDo you think it useful to learn English with the help of some strategies?ⅡWhat strategies do you think can be employed in English learning?2.Global reading:Text organizationPart1(paras1-2):While you cannot expect to learn English well without hard work,there are various helpful learning strategies..Part2(paras3-8):Six useful strategies for learning English.Part3(paras9):A balance between input and output is important.3.Detailed reading:difficult sentences analysis,language study andpractice(See lecture notes);age:according to5.Structure---not only…but also,it’s true that…,but;–ment&–ion(also–ation,-ition,-sion)6.Home reading:How I Improve Your Study Habit1)Main information;2)Text organization;3)Reflections on the text.课后作业(Assignments)1.Topic for writing:How you plan to develop your listeningcomprehension and speaking ability at college2.Home reading:How I Improve Your Study Habits;3.Prepare Unit2主要参考资料(References)Longman Dictionary of English Language and Culture.Longman Group UK.Oxford Advanced English Dictionary.Oxford University Press College English(Third edition)Intensive Reading1Teacher’s Book 《新英汉词典》.上海译文出版社章振邦主编.《新编英语语法教程》.上海:上海外语教育出版社,1999.张道真.《现代英语用法词典》.上海:上海译文出版社,1983.备注(Notes)任课教师签名：Lecture NotesBefore Reading:Introductory RemarksIn a sense,English is not teachable,but learnable.The text we are going to read today presents some useful tips passed down to us by experienced language learners. Let’s read the text together to find out what they are.Besides,I believe you all have some individual experiences to add.Warming-up1.DiscussionTeacher:Before we study the text,let me ask you some questions.1)Do you think it useful to learn English with the help of some strategies?2)What strategies do you think can be employed in English learning?2.Questions about the TextBased on the title,guess what the text is about.Question:What are language learning strategies?rmation Related to the Text1)Possible Language Learning StrategiesPossible language learning strategies include:using practice opportunities, self-evaluation,selective attention,time management,reviewing notes taken in class and checking one’s understanding,constantly seeking answers to questions instead of passively receiving information,etc.2)Pen PalA pen pal is a friend writing from a different country,language,and culture.Pen pals offer a good opportunity to practice a foreign language,to exchange opinions, compare points of views and learn about places and people thousands of kilometers away from you.Those pen pals who write emails to each other are also known as key pals or web pals.Global ReadingComprehension of the Text1.True or False JudgmentDirections:The following is a set of statements about the text.If a statement is true, repeat it;if it is false,make necessary changes to turn it into a true one.1)Language learners should memorize all the new words.(F)(While active words demand constant practice and memorization,words that do not often occur in everyday situations require just a nodding acquaintance.)2)It’s impossible to cram too many words into your head at a time.(T)3)The meaning of a word and the way native speakers use it are equally important.(T)4)Listening to English occasionally will improve your ear and speaking skills.(F) (One must listen to English on a regular basis.)5)It’s important to catch every detail in English listening comprehension.(F)(The first time one may not catch a great deal,but with each repetition one will get something more.)6)Language learners do not find many opportunities to practice oral English at school. (T)7)Rehearsing aloud is a useful way to practice spoken English.(T)8)Reading is the only reliable source of language input.(F)(Reading is the main and most reliable source of language input.)9)There are various ways like keeping an English diary or writing to a pen pal to keep writing in English regularly.(T)10)Reading and listening are more important in language learning than speaking and writing.(F)(A balance between input and output is important.)2.Answer the following questions based on the text:1)What does it take to learn English well?2)How can you make the task of learning English easier?3)What is the most effective route to enlarging your vocabulary?4)What is the second language strategy suggested by the author?5)Why is it important to listen to English every day?6)According to the author,what is the easiest way to practice speaking English?And why?7)Why is it important to read widely?8)What kind of materials should you include in your wide reading?9)Apart from your teacher’s writing assignment,what other ways of writing does the author suggest?10)What is the author’s conclusion at the end of the article?Text Organization1.What type is the text?A.narrationB.expositionC.descriptionD.argumentationKey(B)2.Analyze the structure of the textpart paragraphs Main idea11-2While you cannot expect to learn English well without hardwork,there are various helpful learning strategies.23-8Six useful strategies for learning English.39A balance between input and output is important.Words&Expressionsoffer:n.提议,提供(物),录取通知书v.提供；提议做某事，表示愿意做某事I’m sorry I can’t accept your offer.Can you offer your help?She offered to teach me English.Para.1by no means:not at all决不I am by no means satisfied with your present performance.Para.21.nevertheless:adv.however,in spite of,still然而，尽管如此Of course,she didn’t understand what her parents were quarreling about,but she was scared nevertheless.2.while:conj.although,even though尽管While I quite understand why he refused to help her,I cannot agree that he was right not to do so.4.Nevertheless,while you cannot expect to gain a good command of Englishwithout sustained hard work,there are various helpful learning strategies you can employ to make the task easier.:Although you have to work hard continually in order to be good at English,you can also make use of some learning strategies to help you reach your goal.Para.3plain of/about:抱怨,投诉街坊邻居们向警方投诉工地上传来的噪音。
Homework Assignment – Week 1 - Answers
Homework Assignment – Week 1Chapter 11-Why are financial markets important to the health of the economy?Because they channel funds from those who do not have a productiveuse for them to those who do, thereby resulting in higher economicefficiency.2-When interest rates rise, how might businesses and consumers change their economic behavior?Businesses would cut investment spending because the cost offinancing this spending is now higher, and consumers would be lesslikely to purchase a house or a car because the cost of financing theirpurchase is higher.3-How can a change in interest rates affect the profitability of financial institutions?A change in interest rates affects the cost of acquiring funds forfinancial institution as well as changes the income on assets such asloans, both of which affect profits. In addition, changes in interestrates affect the price of assets such as stock and bonds that thefinancial institution owns that can lead to profits or losses.4-Is everybody worse off when interest rates rise?No. People who borrow to purchase a house or a car are worse offbecause it costs them more to finance their purchase; however, saversbenefit because they can earn higher interest rates on their savings.5-What effect might a fall in stock prices have on business investment?The lower price for a firm’s shares means that it can raise a smalleramount of funds, and so investment in plant and equipment will fall.6-What effect might a rise in stock prices have on consumers’ de cisions to spend?Highe r stock prices mean that consumers’ wealth is higher and sothey will be more likely to increase their spending.7-How does a decline in the value of pound sterling affect British consumers?It makes foreign goods more expensive and so British consumers willbuy less foreign goods and more domestic goods.8-How does an increase in the value of the pound sterling affect American businesses?It makes British goods more expensive relative to American goods.American businesses will find it easier to sell their goods in the UnitedStates and abroad, and the demand for their products will rise. If,however, an American business depends on supplies/parts fromBritish companies these products will increase their costs.9-How can changes in foreign exchange rates affect the profitability of financial institutions?Changes in foreign exchange rates change the value of assets held byfinancial institutions and thus lead to gains and losses on these assets.Also changes in foreign exchange rates affect the profits made bytraders in foreign exchange who work for financial institutions.10-U sing find a chart of the US dollar vs. British Pound exchange rate for the past 5 years. In what year would an American have found it cheapest to visit London? In what year would an English citizenhave found it cheapest to visit the Grand Canyon?The exchange rate chart can be found at:/quote/GBPUSD:CUR/chart. The Poundwas the weakest in 2009 and this would have been the cheapest timefor an American to visit London. The Pound was strongest inNovember 2007 and this would have been the time when an EnglishCitizen would have found the US the cheapest.11-W hat is the basic activity of banks?Banks accept deposits and then use the resulting funds to make loans. 12-W hat are other important financial intermediaries in the economy besides banks?Savings and loan associations, mutual savings banks, credit unions,insurance companies, mutual funds, pension funds, and financecompanies13-C an you think of any financial innovation in the past 10 years that has affected you personally? Has it made you better or worse off? In what way? 14-W hat types of risks do financial institutions face?The profitability of financial institutions is affected by changes ininterest rates, stock prices, and foreign exchange rates; fluctuations inthese variables expose these institutions to risk. Financial institutionsalso face credit risk to counterparties with whom the trade and clientsto whom they lend.15-W hy do managers of financial institutions care so much about the activities of the Federal Reserve System?Because the actions of the Federal Reserve affects interest rates,inflation, and business cycles, all of which have an important impacton the profitability of financial institutions.16-The following table lists foreign exchange rates between U.S. dollars andBritish pounds during April:Date U.S.Dollarsper GBP Date U.S.Dollarsper GBP4/1 1.9564 4/18 1.7504 4/4 1.9293 4/19 1.7255 4/5 1.914 4/20 1.6914 4/6 1.9374 4/21 1.672 4/7 1.961 4/22 1.66844/8 1.8925 4/25 1.66744/11 1.8822 4/26 1.68574/12 1.8558 4/27 1.69254/13 1.796 4/28 1.72014/14 1.7902 4/29 1.75124/15 1.7785Which day would have been the best day to convert $200 into British pounds? The best day is 4/25. At a rate of $1.6674/pound, you would have£119.95.Which day would have been the worst day? What would be the difference in pounds? The worst day is 4/7. At $1.961/pound, you wouldhave £101.99, or a difference of £17.96.Chapter 21.Why is a share of Microsoft common stock an asset for its owner and aliability for Microsoft?The share of Microsoft stock is an asset for its owner because itentitles the owner to a share of the earnings and assets of Microsoft.The share is a liability for Microsoft because it is a claim on itsearnings and assets by the owner of the share.2.If I can buy a car today for $5,000 and it is worth $10,000 in extra incomenext year to me because it enables me to get a job as a traveling anvil sellershould I take out a loan from Larry the loan shark at 90% interest rate if noone else will give me a loan? Will I be better or worse off as a result of taking out this loan? Can you make a case for legalizing loan-sharking?Yes, I should take out the loan, because I will be better off as a result ofdoing so. My interest payment will be $4,500 (90% of $5,000), but as aresult, I will earn an additional $10,000, so I will be ahead of the gameby $500. Since Larry’s loan-sharking business can make some peoplebetter off, as in this example, loan sharking may have social benefits.(One argument against legalizing loan sharking, however, is that it isfrequently a violent activity.)3.Some economists suspect that one of the reasons that economies indeveloping countries grow so slowly is that they do not have well-developed financial markets. Does this argument make sense?Yes, because the absence of financial markets means that funds cannotbe channeled to people who have the most productive use for them.Entrepreneurs then cannot acquire funds to set up businesses thatwould help the economy grow.4.“Because corporations do not actually raise any funds in secondary markets,they are less important to the economy th an primary markets.” Comment.This statement is false. Prices in secondary markets determine theprices that firms issuing securities receive in primary markets. Inaddition, secondary markets make securities more liquid and thuseasier to sell in the primary markets. Therefore, secondary marketsare, if anything, more important than primary markets.5.If you suspect that a company will go bankrupt next year, which would yourather hold, bonds issued by the company or equities issued by the company?Why?You would rather hold bonds, because bondholders are paid offbefore equity holders, who are the residual claimants.6.How can the adverse selection problem explain why you are more likely tomake a loan to a family member than to a stranger?Because you know your family member better than a stranger, youknow more about the borrower’s honesty, propensity for risk taking,and other traits. There is less asymmetric information than witha stranger and less likelihood of an adverse selection problem, withthe result that you are more likely to lend to the family member.7.Think of one example in which you have had to deal with the adverseselection problem.8.Why do loan sharks worry less about moral hazard in connection with theirborrowers than some other lenders do?Loan sharks can threaten their borrowers with bodily harm ifborrowers take actions that might jeopardize paying off the loan.Hence borrowers from a loan shark are less likely to engage inmoral hazard.9.If you are an employer, what kinds of moral hazard problems might youworry about with your employees?You would be concerned that they would carry out theirresponsibilities – removing a poorly performing employee is anexpensive endeavor. They might steal or commit fraud.10.If there were no asymmetry in the information that a borrower and a lenderhad, could there still be a moral hazard problem?Yes, because even if you know that a borrower is taking actions thatmight jeopardize paying off the loan, you must still stop the borrowerfrom doing so. Because that may be costly, you may not spend thetime and effort to reduce moral hazard, and so moral hazard remainsa problem.11.“In a world without information and transaction costs, financialintermediaries would not exist.” Is this statement true, false or un certain?Explain your answer.By looking at the three reasons for financial intermediaries to existone can see that this deals with the transaction costs and adverseselection issues. Risk sharing may still be an issue. A small investormay not be able to build a well-diversified portfolio and thus afinancial intermediary may be necessary to construct this for him.12.Why might you be willing to make a loan to your neighbor by putting funds ina savings account earning a 5% interest rate at the bank and having the banklend her the funds at a 10% interest rate rather than lend her the fundsyourself?Because the costs of making the loan to your neighbor are high (legalfees, fees for a credit check, and so on), you will probably not be ableto earn 5% on the loan after your expenses even though it has a 10%interest rate. You are better off depositing your savings with afinancial intermediary and earning 5% interest. In addition, you arelikely to bear less risk by depositing your savings at the bank ratherthan lending them to your neighbor.13.How does risk sharing benefit both financial intermediaries and privateinvestors?Risk sharing benefits financial intermediaries because they are able toearn a spread between the returns they earn on risky assets and theyreturns they pay on the less-risky assets they sell. Investors benefitbecause they are able to invest in a better diversified portfolio thenwould otherwise be available.14.Discuss some of the manifestations of the globalization of world capitalmarkets.Increasing globalization of financial intermediaries such as banks andother institutions. Interconnectedness of financial markets such asstock markets etc (one can observe a high degree of correlationbetween these). Also disruption in a major foreign market can causedisruption in the US and vice versa.Extra Questions:•Think about investments on .–Quite a bit of information can be found either on the website or in the prospectus -/Downloads/Legal/Prosper_Prospectus_2012-07-19.pdf–What potential returns are described on the website?–Returns range from 5.24% for AA rated borrowers to 14.75% for HR rated borrowers. Lending is for periods of 1, 3 or 5 years with only 3years being available to HR.–What are the significant risks to investing?–’s prospectus from pages 22-45 lists many different risks.Here are several - there is interest rate risk. If you lend at 7% andinterest rates go to 10% then on a present value basis you will havelost money. There is credit risk – first you are lending on anunsecured basis, second it is not clear what happens to your loan if goes under. There is asymmetric information risk – theinformation that the borrower gives to take out the loan is not verified.There is liquidity risk. There is a secondary market but it is not clearwhether it is liquid. There is also prepayment risk – the risk that aborrower pays back the loan early. To think about this risk imaginethat you have lent money at 10% and then interest rates fall to 5%halfway through the life of the loan. If the borrower prepays the loanthen you will only be able to reinvest the money at a similar yield bytaking on additional risk.–When investing through the website what does one buy?–An investor is buying a “Borrower Payment Dependent Note.” This information can be found in the prospectus. will issuethe notes–On the website are large numbers of borrowers seeking funds. What alternatives might these borrowers have for raising funds? Whatreasons might drive them to raise funds here over those alternatives?–Several main alternatives to would be other peer-2-peer lending sites, banks, credit unions and other retail based depositoryinstitutions and credit cards. A rational borrower would investigateall of these options as well as for raising funds for theirpurposes. With this assumption it could be that funds are moreexpensive or unavailable through these other sources or that is a cheaper source of funds than these other sources.–Is there a secondary market for an investment on ? How does it work?–Yes, advertises a service they call FOLIO in which one can list notes that you own and want to sell.•On the website look up information about the fund VFISX. Within the summary prospectus find:–Over the past 10 years what are the max and min annual return for this fund?–Max is 7.89% in 2007 and min is 1.03% in 2004.–What are the significant risks for investing in this fund?–Income risk – the risk that changes in market rates will reduce the income available to the fund. Interest rate risk – this risk that changesin interest rates will cause bonds held in the fund to change in value.Manager risk – the risk that poor security selection on the part of themanager will cause poor investment returns relative to otherpotential investments.。
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Assignment1True/FalseIndicate whether the statement is true or false.__T__ 1. A transaction is an exchange of value.__F__ 2. Business-to-consumer electronic commerce occurs when a person sells an item through a Web auction site to another person.__T__ 3. The U.S. government is one of the largest EDI trading partners in the world.__T__ 4. Firms such as Wal-Mart and General Electric have been pioneers in using EDI to improve their purchasing processes and their relationships with suppliers.__T__ 5. In some cases, business processes use traditional commerce activities very effectively, and technology cannot improve upon them.__T__ 6. Electronic commerce provides buyers with an easy way to customize the level of detail in the information they obtain about a prospective purchase.__T__ 7. Businesses and individuals can use electronic commerce to reduce transaction costs by improving the flow of information and increasing the coordination of actions.__T__ 8. Using the value chain reinforces the idea that electronic commerce should be a business solution, not technology implemented for its own sake.Multiple ChoiceIdentify the choice that best completes the statement or answers the question.__b__ 9. The group of logical, related, and sequential activities and transactions in which businesses engage are often collectively referred to as business ____.a. services c. logisticsb. processes d. communications__c__ 10. A(n) ____ is a specific collection of business processes used to identify customers, market to those customers, and generate sales to those customers.a. industry value chain c. revenue modelb. strategic alliance d. value-added network__a__ 11. Businesses often calculate ____ numbers before committing to any new technology.a. return-on-investment c. productivityb. return-to-profit d. return-to-value__d__ 12. In a ____, companies coordinate their strategies, resources, and skill sets by forming long-term, stable relationships with other companies and individuals based on shared purposes.a. market economic structure c. business modelb. value system d. network economic structure__c__ 13. Strategic partnerships occurring between or among companies operating on the Internet are called ____.a. strategic alliances c. virtual companiesb. economic structure d. virtual partnerships__b__ 14. As more people participate in a network, the value of the network to each participant increases. This is known as the ____.a. law of diminishing returns c. listing effectb. network effect d. fax effect__c__ 15. A ____ is a way of organizing the activities that each strategic business unit undertakes to design, produce, promote, market, deliver, and support the products or services it sells.a. supply chain c. value chainb. supply group d. value group__c__ 16. SWOT is the acronym for ____.a. supply, wealth, occupations, and threatsb. supply, weaknesses, opportunities, and testingc. strengths, weaknesses, opportunities, and threatsd. strengths, wealth, occupations, and testingCompletionComplete each statement.17. In the first wave of electronic commerce, __________English__________ was the dominant language usedon most Web sites.18. A combination of ___________electronic_________ and traditional commerce strategies works best whenthe business process includes both commodity and personal inspection elements.19. A(n) __________virtual community__________ is a gathering of people who share a common interest, whichtakes place on the Internet.20. A(n) __________strategic business__________ unit is an autonomous part of a company that is large enoughto manage itself but small enough to respond quickly to changes in its business environment.21. The law of __________diminishing__________ returns says that most activities yield less value as theamount of consumption increases.22. Your e-mail account, which gives you access to a network of other people with e-mail accounts, is anexample of a(n) __________network__________ effect.23. Internet e-mail accounts are far more valuable than single-organization e-mail accounts because of the__________network effect__________.24. Internet __________infrastructure__________ includes the computers and software connected to the Internetand the communications networks over which the message packets travel.Essay25. What are the results of ’s SWOT analysis?优势：1、方便快捷，服务优势增加2、产品齐全3、降低商品的价格4、基础设施建设费用少劣势：1、网络购物的方式满足不了用户的消费心理2、诚信制度尚未完善3、物流配送不完善4、缺少增值服务5、利润偏低机会：1、信息技术发展迅速2、电子商务联盟3、电子商务整体环境日渐完善威胁：1、安全问题2、法律不完善3、竞争激烈26. What types of business processes are well suited to electronic commerce?The following business processes are well suited to electronic commerce:Sale/purchase of books and CDs, sale/purchase of goods that have strong brand reputations, online delivery of software and digital content, sale/purchase of travel services, online shipment tracking, and sale/purchase of investment and insurance products.。