1-1&2约束及约束方程、自由度和广义坐标
小学数学《几分之一》课件
2块
平均分
1 2
—12
把一个饼平均分成两份，每份是它的
1 2
如果像这样分，能不能用二分之一表示？
下面哪些图形的阴影部分可以
用
1 2
表示？
（1） （√ ）
（2） ( ×)
（3） ( ×)
请折出长方形的 1 。
2
同桌交流： 1
你是怎样折出长方形的 2 的。 哪部分是长方形的 1 ？
用分数表示下面各图中的阴影部 分
1 （ ） 3 ————
（）
1 （ ）
————
5 （ ）
1 （ ）
————
6 （ ）
1 （ ）
————
4 （ ）
1 3
1 2
用分数表示每个图里的涂色部分。
1
1
3
3
看图估一估，填上合适的分数。
1
—12 —13 —16
一堆小棒有12根。分别拿出这
堆
11
小棒的 2 和 3 。
（ 3）
平均分成6份， 每份是这堆苹果的（（16 ） ）。
1 2
1 3
1 6
阴影部分是1个圆的 1
4
阴影部分是8个圆的
1 4
折一折，涂一涂,说一说。 拿出自己手中的纸，折出它的四分之一。
同桌交流：你把什么图形平均分成了几份， 每份是这个图形的几分之一？
2、认识 —1 3
—1 3
把一个圆平均分成（ 三份）， 每份是它的（ 三分之一 ），写 作（ —1 ）。
2
分月饼 这块月饼
他们每人分得
月二饼分之一。
1
2
1 2
把一块月饼平均分成
《红色》第一集_导演脚本_20121019
第一集1-1 日 外 上海街道1937年11月中旬，打了三个月的淞沪之战落幕。
国军撤退，日军进入上海，上海街头人潮乱涌。
（徐天人物出场）空荡荡的街道上，徐天从远处独自走来。
（精神世界感受）CG结合实拍：微观世界，无比安静，一滴水从空中划过，重重的摔落在地上，渐起了水花，只有水滴落地的声音。
突然回到自然环境，徐天拎着菜和鱼在大街上行走，菜叶上的水滴纷纷滑落。
纷乱的街道，日本人进入上海的场面，纷乱的声音，与之前的画面形成强烈的反差。
(本场需要做细节设定)有坦克在平民潮里移动，日军在坦克上，间或朝天扫机枪。
人潮更乱，徐天提着一网兜小菜和一条鱼，逆着人流。
他尽量贴铺面街沿，实在走不动，停一会儿再往前。
田丹在乱流里，右手提个行李，被人潮裹得跌跌撞撞。
她围了显眼的红色围巾，左手执着的一张纸条飞了，田丹追了几步，身子再难平衡，往街边跌出来。
徐天拉住她。
高速镜头：那张纸条划过徐天眼前，消失无踪。
1-1.1 日 外 上海街道一角徐天托着田丹一直撞到一家店角才稳住身子。
田丹抬起头：谢谢你……徐天呆了。
一张慌张又淡定，简单又美丽的脸，让徐天瞬间失聪，他设法挪开自己的眼睛。
徐天：找纸条？田丹：……算了。
徐天：三个字？王擎汉，三横王擎天的擎。
田丹多看了徐天一眼，再看了看他手里的小菜：不要了，没关系。
徐天：刚才飘过去，碰巧看见……田丹收拾起行李，继续往前。
徐天只好收了嘴，看田丹远去。
田丹回过身子：你怎么往那边去？徐天：……朋友有急事，再三相召。
田丹：前面都是日军。
徐天：见到朋友就回。
【高速镜头】【田丹回头笑了笑走了】【以下镜头用升格再拍一次，用作闪回】田丹不可思议又无暇多顾的样子，再次裹入乱流。
徐天怔了片刻，看见脚前田丹遗落的围巾。
他抬头看田丹已不见了，犹豫一会儿，迈过围巾往前走。
一会儿，他又挤回来，拣起那条围巾塞入怀里。
1-2 日 内 外滩楼房地下室老向带着六个人宣誓；我志愿加入中国共产党，拥护党的纲领，遵守党的章程，履行党员义务，执行党的决定，严守党的纪律，保守党的秘密，对党忠诚，积极工作，为共产主义奋斗终身，随时准备为党和人民牺牲一切，永不叛党。
一级建造师工程经济计算公式及例题
一级建造师工程经济公式例题例题：某公司借款1000万元，年复利率为10％，试问5年末连本带利一次偿还多少？答：F=P(1+i)n=1000＊（1+10%）5=1610。
51万元（2）掌握一次性支付的现值计算(已知F求P）例题：某公司希望所投资项目5年末有1000万元资金，年复利率为10%，试问现在需一次性投资多少?答：P= F(1+i)-n=1000×（1+10％）—5=620.9万元（3）掌握等额支付系列的终值计算（已知A求F）公式：F=AF=A（F/A,i,n)。
例题：某投资人若10年内每年末存10000元，年利率8%，问10年末本利和为多少？答:F=A=10000×=144870元(4）掌握等额支付系列的现值计算（已知A求P）公式:P=AP=等额支付系列一次性支付(投资）的资金金额A= 年金，等额支付每一次支付的资金金额i= 年、月、季度利率（计息期复利率）n= 计息的期数(A使用的时间）为等额支付系列的现值系数（年金现值系数)，符号表示为:（P/A，i,n）,则计算公式为：P=A(P/A，i，n)。
例题：某投资项目，计算期5年，每年年末等额回收100万元，问在利率为10％时，开始须一次投资多少?答：P=A=100×=379。
08万元1.名义利率与有效利率的换算（1）掌握名义利率的计算公式：r=i×mr=名义利率（一年内计息周期乘以计息周期利率所得的年利率）i=一年内计息周期利率m=一年内的计息周期（一年内计息次数）（2）掌握一年内计息周期利率的计算公式:i = r/mi=一年内计息周期利率r=名义利率(一年内计息周期乘以计息周期利率所得的年利率）m=一年内的计息周期（一年内计息次数）(3)掌握一年实际利率（有效利率）的计算公式:i eff=(1+）m-1i eff=一年实际利率（有效利率）I=该年利息（一年利息和）P=一次性支付（投资）的资金金额r=名义利率（一年内计息周期乘以计息周期利率所得的年利率)m=一年内的计息周期（一年内计息次数）（4）掌握计息周期小于（或等于）资金收付周期时的等值计算例题：现在存款1000元，年利率10%,半年复利一次,问5年末存款金额为多少?答：先计算年有效利率（年实际利率)：i eff=(1+）m—1=（1+10%/2）2—1=10。
英语自考 00595英语阅读(一)201504 真题试卷
全国2015年4月高等教育自学考试英语阅读(一)试题课程代码：00595第一部分选择题I. CAREFUL READINGRead the following passages carefully. Decide on the best answer and blacken the corresponding letter on the ANSWER SHEET. (40 points, 2 points each)Passage 1Questions 1 to 5 are based on the following passage.The average population density of the world is 47 persons per square mile. Continental densities range from no permanent inhabitants in Antarctica to 211 per square mile in Europe. In the western hemisphere, population densities range from 4 per square mile in Canada to 675 per square mile in Puerto Rico. In Europe the range is from 4 per square mile in Iceland to 831 per square mile in the Netherlands. Within countries there are wide variations of population densities. For example，in Egypt，the average is 55 persons per square mile,but 1, 300 persons inhabit each square mile in settled portions where the land is arable (可耕种的).High population densities generally occur in regions of developed industrialization, such as the Netherlands, Belgium, and Great Britain, or where lands are intensively used for agriculture, as in Puerto Rico and Java.Low average population densities，which are characteristic of most underdeveloped countries, are generally associated with a relatively low percentage of cultivated land. This generally results from poor quality lands. It may also be due to natural obstacles to cultivation, such as deserts, mountains or malaria-infested jungles; to land uses other than cultivation, as pasture and forested land; to primitive methods that limit cultivation; to social obstacles; and to land ownership systems which keep land out of production.More economically advanced countries of low population density have, as a rule, large proportions of their populations living in urban areas. Their rural population densities are usually very low. Poorer developed countries of correspondingly low general population density, on the other hand, often have a concentration of rural population living on arable land, which is as great as the rural concentration found in the most densely populated industrial countries.1.Which of the following would be the best title for this passage?A. World PopulationB. Population DensitiesC. Population MigrationD. Economics and Population2.In the cultivated areas of Egypt, we may expect to find_____.A.few inhabitantsB.densely populated settlementsC.l,300persons living in one settlementD.55 persons inhabiting one square mile3.The most densely populated community in Europe is_____ .A.IcelandB. BelgiumC.the NetherlandsD. Great Britain4.This passage indicates that Puerto Rico is_____.A.agriculture-orientedB. malaria-infestedC.highly industrializedD. poverty-stricken5.This passage has probably been taken from a/an _____.A.tourist guideB. business journalC.world geography bookD. economic reportPassage 2Questions 6 to 10 are based on the following passage.Engaging in a hobby like reading a book, making a patchwork quilt or even playing computer games can delay the onset of dementia, a US study suggests. Watching TV, however, does not count—and indeed, spending significant periods of time in front of the box may speed up memory loss, researchers found. Nearly 200 people aged 70 to 89 with mild memory problems were compared with a group who had no impairment. The researchers from the Mayo Clinic in Minnesota asked the volunteers about their daily activities within the past year and how mentally active they had been between the age of 50 to 65. Those who had? during middle age, been busy reading, playing games or engaging in craft hobbies like patchworking or knitting were found to have a 40% reduced risk of memory impairment. In later life，those same activities reduced the risk by a rate between 30% and 50%. Those who watched TV for less than 7 hours a day were also 50% less likely to develop memory loss than those who spend longer staring at the screen.“This study is exciting because it demonstrates that ageing does not need to be a passive process，”said neuroscientist Dr. Yonas Geda. “By simply engaging in cognitive exercise, you can protect against future memory loss. Of course, the challenge with this type of research is that we are relying on past memories of the subjects (实验对象)，therefore we need to confirm these findings with additional research.”Sarah Day，head of public health at the Alzheimer’s Society，said，“One million people will develop dementia in the next 10 years so there is a desperate need to find ways to prevent dementia. Exercising and challenging your brain~by learning new skills, doing puzzles such as crosswords, and even learning a new language—can be fun. However, more research, where people are followed up over time, is needed to understand whether these sorts of activities can reduce the risk of dementia.”6.If one suffers from dementia, he would be unable to_____.A. move his limbsB. speak correctlyC. recall past eventsD. sit in upright posture7.The subjects of the research mentioned in the passage were_____.A. people watching TV programs several hours a dayB. the middle-aged with lots of daily mental activitiesC. people actively engaged in their hobbies at an early ageD. two groups of seniors either with or without memory problems8.It was found in the research that_____.A.cognitive exercise helps people prevent future memory lossB.cure for dementia will soon be available in 10 years or soC.mentally challenging hobbies usually lead to mental fatigueD.nothing can deter the gradual loss of memory9.The research was based on the data of the_____.A.brain makeup of the subjectsB.past memories of the subjectses of language of the subjectsD.physical exercises of the subjects10. More research should be conducted in which .A.people of different age groups should be investigatedB.the relationship between dementia and genes will be investigatedC.more subjects will be included so as to verify the current findingsD.effects of cognitive exercise on subjects should be traced over timePassage 3Questions 11 to 15 are based on the following passage.The complex topic “social class”is difficult to avoid when discussing British society，which is often seen as a society in which “social class”is more important than in other countries. This is true to a certain extent, but should probably not be exaggerated. Most countries have some kind of class structure. There exist broad groups within society which share types of employment, income levels, and certain cultural characteristics. But important in the idea of “class” is that it makes a difference to an in dividual’s “life-chances” which group or class he or she is bom into. So if a middle-class couple, perhaps a doctor and a teacher, have a child, it is more likely that that child will also acquire middle-class education, employment and income levels than will the child of working-class factory workers. This is certainly the case in the UK, though it should be stressed that it is far from impossible for the working-class child to acquire middle-class status: it is simply statistically much more unlikely than for his middle-class school-friend.If asked, about half the British population would describe themselves as middle-class, and half as working-class. Employment would be the main guide they would use: manual (or “blue-collar”）workers would usually call themselves working-class，and office (or “white-collar”）workers would usually call themselves middle-class. However, there is a hazy area around unskilled office-work and skilled well-paid manual work which leads to sub-divisions such as “lower middle class”being used; and the term “upper middl e class” might be used to describe doctors and lawyers and so on who have relatively high incomes and high status professions—especially in families with long traditions of such employment. This would differentiate them from the majority of middle-class people today, most of whom have working-class parents orgrandparents. This reflects the huge expansion of the middle class over the twentieth century，and especially since 1945, when more equal social policies were adopted by the government.11.The author discusses British society from the perspective of_____.A. educationB. social classC. employmentD. income levels12.“Class” is important because it____.A.determines an individual’s personalityB.makes a difference to a n individual’s marriageC.makes a difference to the opportunities available to an individualD. gives an individual equal chances for education and employment13.The British would distinguish their social classes mainly by____.A. employmentB. income levelsC. family traditionsD. education backgrounds14.British doctors and lawyers belong to the____.A. upper middle classB. lower middle classC. upper classD. working class15.The middle-class expanded considerably over the twentieth century mainly because____.A. the British earned more money than beforeB. more people received higher education than beforeC.the number of doctors and lawyers increased sharplyD.the British government introduced more equal social policiesPassage 4Questions 16 to 20 are based on the following passage.“But I can’t save any money.” It’s an excuse I hear a lot from which I detect a note of defiance. In the past few years, it has become increasingly frequent, as more and more Americans make less than we spend, eating up the savings in our homes. The national savings rate is declining. And the situation seems to be getting worse.We certainly know that saving money is good for us. Yet saving for tomorrow is still a largely ignored and unappreciated skill. The question tha t naturally follows is: Why? Why don’t Americans make saving a priority?To start with, saving today is much harder. The typical household income has held largely steady for a good half decade, while prices have continued to rise. If you’re having to spend a disproportionate amount of income on food and gas,it’s hard to save. Besides, credit became too accessible. For years it was simply too easy to get your hands on money to spend. While banks at one time would not let you spend more than 36 percent of your total income on debt, they stretched that number to 55 percent during the housing boom. Why save when you could get that big flat-screen TV today and pay for it with mortgage debt that was both cheap and deductible? Last but not least, saving is, was, and always will be no fun. Think about it this way: Choosing to save almost always means opting for delayed gratification instead of immediate gratification. Thepleasure of getting something good today is much greater than that in the future—even if the reward in the future is bigger.Recently, neuroeconomists, a relatively new breed of experts in economics and neuroscience，have started using MRIs (核磁共振成像）to view the brain as it is making money choices. When something we want to buy comes into view, they see the pleasure center firing up. Similarly, getting a few dollars today is more thrilling than getting a slightly larger profit tomorrow. And if you have to wait a few months for that gain, it will have to be much bigger in order to arouse the same interest in your brain. Things way off in the future---like retirement—don’t jostle the pleasure center much at all.16.In the author’s eyes，Americans say they can’t save any money because they_____.A. want to win sympathyB. are well prepared for retirementC.will make more money in the futureD.are probably unwilling to be economical17.According to the passage, during the housing boom the banks _____.A. raised the saving interest rateB. issued fewer credit cardsC. made it easier to borrow moneyD. initiated credit risk management18. How many reasons are given in Paragraph 3?A. 2.B. 3.C. 4.D. 5.19. The neuroeconomists' research is cited to prove_____.A.saving will be more thrilling as time goes byB.MRIs help customers make purchase decisionsC.if s a complex process to stimulate the pleasure centerD.immediate gratification is more appealing than delayed gratification20.What suggestion do you think the author is most likely to give in the following paragraphs?A. Saving up money.B. Applying for credit cards.C. Stimulating consumption.D. Studying the pleasure center.II. SPEED READINGSkim or scan the following passages, and then decide on the best answer and blacken the corresponding letter on the ANSWER SHEET. (10 points, 1 point each)Passage 5Questions 21 to 25 are based on the following passage.Many editors and writers today define flash fiction as a story ranging from a few words to not usually over 1,500 to 2,000 words (but more often less than 1,000 words). A traditional short story ranges from 3,000 to 20,000 words, so flash fiction is considerably shorter. However, while length can help identify flash fiction, it is of little use in actually defining it.The amorphous and variable quality of flash fiction allows for the constant changing of shapes as these stories draw anddevelop from various genres and traditions to create stand-alone stories that often work on their own terms. Countless writers are involved in writing flash fiction in various ways. Many are involved in following the form’s long tradition，and many others are reinventing the form as they continue to experiment with the boundaries and methods of fiction. These shortest of stories are not always diversions for the moment but are often stories that are profound and memorable—as good fiction of longer lengths can be.Charles Baxter notes in the introduction to Sudden Fiction International: 60 Short Short Stories, 'This form is not about to be summarized by anyone's ideas about it. The stories are on so many various thresholds: they are between poetry and fiction, the story and the sketch, prophecy and reminiscence, the personal and the crowd As a form，they are open，and exist in a state of potential.”Some names for flash fiction are chosen to stress brevity, suggesting that such stories can be read or even written in a flash. Other names are chosen to emphasize the way in which the stories affect and enlighten readers. And still other names are chosen for the way in which they cause readers to perform the act of reading, many times forcing them to slow down and read such pieces as slowly and carefully as they would read good poetry.Even though this type of writing travels by several names, flash fiction has become the most popular label, likely because of its snappy poetic consonance, which makes it easy to hold in memory, and because of its distance from the older, less descriptive term “short-shorts”. More and more writers，editors, and readers use “flash fiction”to refer to very short stories.21.Flash fiction usually refers to a story ranging from a few words to____.A.less than 1，000 wordsB. more than 2,000 wordsC.more than 3,000 wordsD. less than 20,000 words22.The form of flash fiction can be best described as____.A.variableB. unifiedC.traditionalD. complete23.How many ways of naming flash fiction are mentioned in Paragraph 4?A. 2.B. 3.C. 4.D. 5.24.Among all the labels referring to very short stories, the most popular one is____.A.short-shortsB. short storyC.flash fictionD. poetic story25.The passage mainly focuses on flash fiction in terms of its____.A.popularityB. namesC.readersD. poetic qualityPassage 6Questions 26 to 30 are based on the following passage.Most of the work that most people have to do is not in itself interesting, but even such work has certain great advantages. To begin with, it fills a good many hours of the day without the need of deciding what one shall do. Most people, when theyare left free to fill their own time according to their own choice, are at a loss to think of anything sufficiently pleasant to be worth doing. And whatever they decide on, they are troubled by the feeling that something else would have been more pleasant.The second advantage of most paid work and of some unpaid work is that it gives chances of success and opportunities for ambition. In most work success is measured by income, and while the capitalistic society continues, this is inevitable. It is only where the best work is concerned that this measure ceases to be the natural one to apply. The desire that men feel to increase their income is quite as much a desire for success as for the extra comforts that a higher income can procure (获取). However dull work may be，it becomes bearable if it is a means of building up a reputation，whether in the world at large or only in one’s own circle. Continuity of purpose is one of the most essential ingredients of happiness in the long run, and for most men this comes chiefly through their work. In this respect those women whose lives are occupied with housework are much less fortunate than men, or than women who work outside the home. The domesticated wife does not receive wages, has no means of bettering herself, is taken for granted by her husband (who sees practically nothing of what she does), and is valued by him not for her housework but for quite other qualities. Of course this does not apply to those women who are sufficiently well-to-do to make beautiful houses and beautiful gardens and become the envy of their neighbors; but such women are comparatively few. For the great majority, housework cannot bring as much satisfaction as work of other kinds brings to men and to professional women.The satisfaction of killing time and of affording some outlet, however modest, for ambition, belongs to most work, and is sufficient to make even a man whose work is dull happier on the average than a man who has no work at all. But when work is interesting, it is capable of giving satisfaction of a far higher order than mere relief from tedium. The kinds of work in which there is some interest may be arranged in a hierarchy.26.For most people, even uninteresting work has the advantage of_____.A.earning a good nameing up extra energyC.cultivating interest in workD.sparing the need of deciding what to do27.In the capitalistic society, income is usually an indication of_____.A. powerB. wisdomC. rightsD. success28.Dull work can be accepted if it_____.A.offers life insuranceB.foresees a chance for promotionC.offers comfortable working environmentD.offers a chance of building up a reputation29.Most housewives are valued by their husbands for_____.A. making houses beautifulB. making gardens beautifulC.other qualities than their houseworkD.their housework rather than other qualitiespared with a man who has no work,a man with a dull job is generally_____.A. happierB. more boredC. less satisfiedD. less pleasant非选择题部分注意事项：用黑色字迹的签字笔或钢笔将答案写在答题纸上，不能答在试题卷上。
钢琴入门,有一份最全的五线谱基础知识大全
钢琴入门 | 有一份最全的五线谱基础知识大全五线谱是记录音乐的一种语言，是一种记谱方法。
五线谱，顾名思义是由五条平行线组成的，当然还包括每相邻两条平行线之间的“间”。
谱表在五线谱中，由五条平行横线所组成的图形叫做谱表。
谱表有许多种类，比较常用的有高音谱表（又叫G谱表）、低音谱表（又叫F谱表）、大谱表和联合谱表。
谱表不同，各线各间的音高位置就不同。
谱号在五线谱上确定音高的位置——也就是音名位置的符号叫做谱号。
通常用的谱号有三种：调号调：音乐作品或其中某部分，起核心作用的主音及基本音级所构成的音列的音高位置叫做调。
调号：用以标记调的升降记号叫做调号。
一般记在谱号之后拍号之前，转调时则标记在转调处。
音符音符：在乐谱表上表示正在进行的音的长短（也叫“音值”）的符号。
在五线谱上，音符的符头位置越高音也越高，反之符头位置越低音也越低。
附点音符：使它前面的音符的时值延长一半休止符拍号二拍子系统：二拍子系统是以强-弱、强-弱的力度形态进行的拍子系统，常见的二拍子拍号如下：在上方的数字代表一个小节有几拍，下方的数字则代表用几分音符当一拍。
三拍子系统：三拍子系统是以强-弱-弱的力度形态进行的拍子系统，常见的三拍子拍号如下：后拍子系统：后拍子系统是前二者的综合运用，常见的有5拍和7拍两种。
一、简谱到五线谱如图1-1所示，描述了简谱中常见的元素。
图1-1 简谱基本元素任何一首曲子，都可以被分为任意数量的“小节”，用长竖线（分节符）分割。
乐曲使用拍子控制节奏，“拍”是音符历时长短的单位。
一拍的时间由乐曲要求规定，如果要求一分钟60拍，那么一拍就是一秒。
每一小节都是有固定“拍数”的，在简谱最上角描述每小节的拍数。
如4/4拍，含义是“四分音符为一拍，每小节四拍”。
假定我们规定一拍是一秒，那么一个四分音符的持续时间就是一秒，一小节就有四秒。
什么是四分音符呢？我们常见的1（duo）、2（re）、3（me）、4（fa）、5（sol）、6（la）、7（si）、0（休止符，不发音）都是四分音符，它们占用一拍的时间。
小学一年级口算练习题（100以内）
小学一年级口算练习题（100以内）篇六 12－3＝ 12＋6＝ 13－8＝ 14－5＝ 8＋5＝ 11－5＝ 20＋7＝ 16－9＝ 9＋4＝ 18－9＝ 17－8＝ 15－9＝ 17－9＝ 12－7＝ 13－6＝ 14－8＝ 30＋7＝ 12－8＝ 14－6＝ 14＋9＝ 18－10＝ 7＋9＝ 90－3= 60＋23= 35＋40＝ 42＋30＝ 50＋21＝ 35＋30＝ 36－20＝ 37－7＝ 57＋8＝ 80－60＝ 9＋70＝ 71＋9＝ 48＋6＝ 99－6＝ 39＋5＝ 26－3＝ 27＋6＝ 54－8＝
10-10= 11-8= 10-0= 10+0=
小学一年级口算练习题（100以内）篇四 12+60= 93-60= 34+60= 38-20= 26+50= 47+10= 35+50= 88-10= 66-20= 20+10= 90-70= 98-90= 83-60= 11+60= 71-50= 50-40= 76-60= 87-10= 97-10= 22+40= 72-70= 57-30= 12+10= 40+40= 80-60= 42+50= 94-10= 60-10= 23+30= 77-70= 33+30= 98-50= 50-40= 47-30= 75-50= 67-40= 91-10= 65-40= 78-40= 63+30=
故障树分析方法（FTA）
故障树分析⽅法（FTA）⼀、故障树分析法概述故障树分析法（Fault Tree Analysis）是由美国贝尔电话研究所的沃森（Watson）和默恩斯（Mearns）与于1961年⾸次提出并应⽤于分析民兵式导弹发射控制系统的。
其后，波⾳公司的哈斯尔（Hasse）、舒劳德（Schroder）、杰克逊（Jackson）等⼈研制出故障树分析法计算程序，标志着故障树分析法进⼊了以波⾳公司为中⼼的宇航领域。
1974年，美国原⼦能委员会发表了以⿇省理⼯学院（MIT）拉斯穆森（Rasmussen）为⾸的安全组所写的“商⽤轻⽔反堆核电站事故危险性评价”的报告，该报告采⽤了美国国家航空和管理部于60年代发展起来的事件树（ET：Event Tree）和故障树分析⽅法。
这⼀报告的发表引起了各⽅⾯的很⼤反响，并推动了故障树分析法从宇航、化⼯和机械等⼯业领域。
所谓故障树分析，就是⾸先选定某⼀影响最⼤的系统故障作为顶事件，然后将造成系统故障的原因逐级分解为中间事件，直⾄把不能或不需要分解的基本事件作为底事件为⽌，这样就得到了⼀张树状逻辑图，称为故障树。
如图1-1所⽰就是⼀简单的故障树。
这⼀简单故障树表明：作为顶事件的系统故障是由部件A的故障或部件B的故障引起的，⽽部件A的故障可能由元件1引起，也可能由元件2引起，部件B的故障则由元件3和元件4同时发⽣故障时引起，这样，就将引起系统故障的基本原因及影响途径表达得⼀清⼆楚。
更⼀般地说，故障树分析就是以故障树为基础，分析影响顶事件发⽣的底事件种类及其相对影响程度。
故障树分析包括以下⼏个主要步骤：建⽴故障树、故障树的定性分析和故障树的定量分析。
图1-1 简单的故障树⼆、故障树的建⽴故障树的建⽴有⼈⼯建树和计算机建树两类⽅法，它们的思路相同，都是⾸先确定顶事件，建⽴边界条件，通过逐级分解得到的原始故障树，然后将原始故障树进⾏简化，得到最终的故障树，供后续的分析计算⽤。
1、确定顶事件在故障诊断中，顶事件本⾝就是诊断对象的系统级（总体的）故障部件。
人教版数学七年级上册 第一章 有理数 单元学习评价卷【含答案】
人教版数学七年级上册 第一章 有理数 单元学习评价卷（）一、单选题（每小题3分，共36分）1．如果温度上升1℃记作℃，那么温度下降5℃，应记作（ ）1+A ．℃B ．℃C ．℃D ．℃5+5-6+6-2．下列语句中正确的有 （）① 所有整数都是正数；② 所有正数都是整数；③ 自然数都是正数；④ 分数是有理数；⑤ 在有理数中除了正数就是负数．A ． 个B ． 个C ． 个D ． 个12343．实数a 、b 在数轴上的位置如图，则等于 a b ab+--()A ．2aB ．2bC ．D ．2b 2a-2b 2a+4．一个数的相反数是非负数，这个数一定是（ ）A ．零B ．负数C ．正数D ．非正数5．下列语句：①一个数的绝对值一定最正数；②一定是负数；③没有绝对值是的数；a -3-④若一个数的绝对值是它本身，那么它一定是正数；⑤在数轴左半轴上离开原点越远的数就越小；⑥一个数比它的相反数大，这个数是非负数．其中正确的个数有（ ）A ．0个B ．3个C ．2个D ．4个6． 如图，数轴上点A ，M ，B 分别表示数a ，，b ，那么原点的位置可能是（）a b +A ．线段AM 上，且靠近点A B ．线段AM 上，且靠近点M C ．线段上，且靠近点BD ．线段上，且靠近点MBM BM 7．能与相加得0的是（ ）3645⎛⎫-- ⎪⎝⎭A ．B ．C ．D ．3645--6354+6354-+3645-+8．下列运算过程中，有错误的是（ ）A ．（3﹣4）×2＝3﹣4×21212B ．﹣4×（﹣7）×（﹣125）＝﹣（4×125×7）C ．9×16＝（10﹣）×16＝160﹣18191191619D ．[3×（﹣25）]×（﹣2）＝3×[（﹣25）×（﹣2）]9．已知数a ，b ，c 的大小关系如图，下列说法：①ab+ac>8；②-a-b+c<0；③；④|a-b|+|c+b|-|a-c|=-2b ；⑤若x 为数轴上任意一个数，则|x-b|+|x-a|的最小1a b ca b c++=-值为a-b ．其中正确结论的个数是（ ）A ．1B ．2C ．3D ．410．按如图所示的运算程序，若输入x =2，y =1，则输出结果为（）A ．1B ．4C ．5D ．911．第七次全国人口普查数据显示，山东省常住人口约为10152.7万人，将101 527 000用科学记数法（精确到十万位）（ ）A ．1.02×108B ．0.102×109C ．1.015×108D ．0.1015×10912．我国第十四个五年规划和2035年远景目标纲要中阐释了“坚持农业农村优先发展，全面推进乡村振兴”的具体目标：坚持最严格的耕地保护制度，实施高标准农田建设工程，建成亿亩集中连片高标准农田，下列关于亿的说法正确的是（ ）10.7510.75A ．亿是精确到亿位10.75B ．亿是精确到十亿位10.75C ．亿用科学记数法表示为，则，10.7510na ⨯ 1.075a =9n =D ．亿用科学记数法表示为，则，10.7510na ⨯10.75a =8n =二、填空题（每小题3分，共24分）13．一袋糖果包装上印有“总质量”的字样．小明拿去称了一下，发现质量为，(5005)g ±497g 则该糖果厂家_____________（填“有”或“没有”）欺诈行为．14．在和1之间的负整数有______个．526-15．已知有理数、满足，则________．a b 2|3|(1)0a b -++=a b +=16．在数轴上，把表示的点移动5个单位长度后，所得对应点的数是______．2-17．计算：1－（＋2）＋3－（＋4）＋5－（＋6）＋…－（＋2014）＝_________．18．从－3、－1、0、＋2、＋4 中，任取 3 个数相乘，则乘积的最大值是________．19．月球沿着一定的轨道围绕地球运动，它的半长轴约为385000千米，这个数据用科学记数法精确到万位表示，应记为________千米．20．用四舍五入法取近似数：2.7982≈ __________（精确到0.01）.三、解答题（本大题共40分）21．（4分）把下面的数填入它所属于的集合的大括号内（填序号）①，②，③20%，④0，⑤，⑥，⑦，⑧5.3-5+27-7-3--∣∣( 1.8)--正数集合｛ ｝整数集合｛ ｝分数集合｛ ｝有理数集合｛ ｝22．（12分）计算：（1）（﹣21）﹣（﹣9）＋（﹣8）﹣（﹣12）；（2）；152()(36)469-+-⨯-（3）；421328()44--⨯-+（4）．32200913(2)(2)2|(1)1|84-⨯-÷--⨯-⨯+23．（4分）已知有理数a 、b 互为相反数，c 、d 互为倒数，m 是平方等于它本身的数，求代数式4（a +b ）﹣（cd ）5+m 的值．24．（4分）计算：已知14m n ==，（1）当时，求的值；0m <m n +（2）求的最大值；-m n 25．（4分）实数a ，b ，c 在数轴上的对应点位置如图：（1）用“<”连接0，a ，b ，c 四个数；（2）化简：①；||||a c b c -+-②．||||a b a c +-+26．（6分）某巡警骑摩托车在一条南北大道上巡逻．某天他从岗亭出发，晚上停留在处，A 规定向北方向为正．当天行驶记录如下（单位：千米）．10,8,6,13,7,12,3,2+-+-+-+-（1）该巡警巡逻时离岗亭最远是多少千米？A（2）在岗亭什么方向？距岗亭多远？（3）若摩托车每行1千米耗油0.05升，那么该摩托车这天巡逻共耗油多少升？327．（6分）已知M、N在数轴上，M对应的数是，点N在M的右边，且距M点4个单位长度，点P、Q是数轴上两个动点：（1）直接写出点N所对应的数；（2）当点P到点M、N的距离之和是5个单位时，求点P所对应的数；（3）如果P、Q分别从点M、N出发，均沿数轴向左运动，点P每秒走2个单位长度，先出发5秒钟，点Q每秒走3个单位长度，当P、Q两点相距2个单位长度时，点P、Q对应的数各是多少？答案1．B解：如果温度上升1℃记作+1℃，即初始温度为0℃，那么温度下降5℃记作-5℃，故选：B．2．A解：①所有整数都是正数，错误，比如-1；②所有正数都是整数，错误，比如0.5；③自然数都是正数，错误，比如0；④分数是有理数，正确；⑤在有理数中除了正数就是负数，错误，还有零；∴正确的有一个；故选A．3．A解：根据实数a、b在数轴上的位置得知：a＜0，b＞0，a+b＞0, a﹣b＜0∴|a+b|=a+b，|a﹣b|=b﹣a，∴|a+b|-|a﹣b|=a+b-b+a=2a，故选A．4．D解：非负数是指正数或 0，而负数的相反数是正数，0 的相反数是 0，所以这个数一定是负数或 0．故选：D．5．C解：①一个数的绝对值一定最非负数，故错误；a-②不一定是负数，有可能为0或正数，故错误；3-③没有绝对值是的数，故正确；④若一个数的绝对值是它本身，那么它一定是正数或0，故错误；⑤在数轴左半轴上离开原点越远的数就越小，没有指明数轴正方向，故错误；⑥一个数比它的相反数大，这个数是非负数，故正确；故选：C．6．A解：∵数轴上点A ，M ，B 分别表示数a ，，b ，a b+∴由它们的位置可得a ＜0，a +b ＞0，b ＞0且|a |＜|b |，∴据此可判断原点在线段AM 上，且靠近点A ．故选：A ．7．C解：方法一：；363636630045454554⎡⎤⎛⎫⎛⎫---=+-=-=-+⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎦方法二：的相反数为；3645⎛⎫-- ⎪⎝⎭3645⎛⎫- ⎪⎝⎭故选：C ．8．A解：A 、原式＝3×2﹣×2＝6﹣9＝﹣3，符合题意；92B 、原式＝﹣（4×125×7），不符合题意；C 、原式＝（10﹣）×16＝160﹣，不符合题意；1191619D 、原式＝3×[（﹣25）×（﹣2）]，不符合题意．故选：A ．9．B解：由题意b ＜0，c ＞a ＞0，|c|＞|b|＞|a|，①b+c ＞0，a （b+c ）=ab+ac ＞0，故原结论正确；②-b ＞0，-a ＜0，则-a-b+c ＞0，故原结论错误；③=1-1+1=1，故原结论错误；||||||a b c b a c ++④a-b ＞0，c+b ＞0，a-c ＜0，则|a-b|+|c+b|-|a-c|=a-b+c+b+a-c=2a ，故原结论错误；⑤|x-b|+|x-a|表示x 到a 和到b 的距离之和，当b≤x≤a 时，|x-b|+|x-a|的值最小，最小值为a-b ，故原结论正确．故正确结论有2个．故选：B ．10．D解：∵是偶数，2x =∴把代入，得：21x y ==，2()x y +原式=22(21)39+==故选：D ．11．C解：8101527000101500000 1.01510≈=⨯．故选：C 12．C解：亿精确到百万位，用科学记数法表示为， 10.7591.0710⨯故选C ．13．没有解：∵总质量（500±5）g ，∴糖果质量在（500+5）g 与（500-5）g 之间都合格，而产品有497g ，在范围内，故合格，∴厂家没有欺诈行为．故没有．14．2解：在和1之间的负整数有：-2，-1，共2个，526-故答案是：215．2解：2|3|(1)0a b -++= 3,1a b ∴==-3(1)2a b ∴+=+-=故2．16．-7或3解：当数轴上-2的对应点向左移动5个单位时，对应点表示数是-2-5=-7；当向右移动5个单位时，对应点表示数-2+5=3．故-7或3．17．﹣1007．解：原式＝[1﹣（+2）]+[3﹣（+4）]+[5﹣（+6）]+…+[2013﹣（+2014）]＝﹣1﹣1﹣1﹣…﹣1＝﹣1007．故﹣1007．18．12解：积最大的是：（-3）×（-1）×（+4）=3×1×4=12．故答案为:12．19．53.910⨯解：5385000390000 3.910≈=⨯故．53.910⨯20．2.80解：∵8>5，∴2.7982≈2.80（精确到0.01）.故2.8021．见解析解：-|-3|=-3，-（-1.8）=1.8．正数集合{②③⑧}整数集合{②④⑥⑦}分数集合{①③⑤⑧}有理数集合{①②③④⑤⑥⑦⑧}．22．（1）-8；（2）-13；（3）；（4）3154-14-解：（1）原式＝﹣21＋9﹣8＋12＝﹣29＋21＝﹣8；（2）原式＝﹣×（﹣36）＋ ×（﹣36）﹣ ×（﹣36）145629＝9﹣30＋8＝﹣13；（3）原式＝﹣16﹣8×＋ 11634＝﹣16﹣＋ 1234＝﹣15 ；34（4）原式＝﹣×（﹣8）÷4﹣2×1814＝ 11-42＝﹣．1423．﹣1或0解：∵a 、b 互为相反数，∴a +b ＝0，∵c 、d 互为倒数，∴cd ＝1，又∵m 是平方等于它本身的数，∴m ＝0或1，当m ＝0时，原式＝4×0﹣15+0＝﹣1；当m ＝1时，原式＝4×0﹣15+1＝0．故1或0．24．（1）3或-5；（2）5解：∵|m |=1，|n |=4，∴m =±1，n =±4；（1）∵m ＜0，∴m =-1，n =-4或m =-1，n =4，∴m +n =3或-5；（2）当m =1，n =4时，m -n =-3；当m =-1，n =-4时，m -n =3；当m =1，n =-4时，m -n =5；当m =-1，n =4时，m -n =-5；∴m -n 的最大值是5．25．（1）c ＜a ＜0＜b ；（2）①；②2a b c +-2a b c++解：（1）由题意可得，c ＜a ＜0＜b ；（2）∵c ＜a ＜0＜b ，|a |＜|b |，①||||a cbc -+-=a c b c-+-=；2a b c +-②||||a b a c +-+=a b a c+++=2a b c++26．（1）10；（2）A 在岗亭的南方，距岗亭9千米；（3）3.05．解：（1）每次巡逻后离岗亭的距离为10千米，10-8=2千米，10-8+6=8千米，10-8+6-13=-5千米，10-8+6-13+7=2千米，10-8+6-13+7-12=-10千米，10-8+6-13+7-12+3=-7千米，10-8+6-13+7-12+3-2=-9千米，答：巡警巡逻时离岗亭最远是10干米．（2）10-8+6-13+7-12+3-2=-9（千米）答：A在岗亭的南方，距岗亭9千米．（3）0.05×（10+8+6+13+7+12+3+2）=0.05×61=3.05（升）答：摩托车这天巡逻共耗油3.05升．27．（1）1；（2）-3.5或1.5；（3）点P对应-37，点Q对应-35或点P对应-45，点Q对应-47解：（1）-3+4=1．故点N所对应的数是1；（2）（5-4）÷2=0.5，①点P在点M的左边：-3-0.5=-3.5，②点P在点N的右边：1+0.5=1.5．故点P所对应的数是-3.5或1.5．（3）①点P在点Q的左边：（4+2×5-2）÷（3-2）=12÷1=12（秒），点P对应的数是-3-5×2-12×2=-37，点Q对应的数是-37+2=-35；②点P在点Q的右边：（4+2×5+2）÷（3-2）=16÷1=16（秒）；点P对应的数是-3-5×2-16×2=-45，点Q对应的数是-45-2=-47．。
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§1-2 自由度和广义坐标
确定具有完整约束质点系的位置的独立参数的个数称为 质点系的自由度数。 质点系的自由度数。 例如，图1 例如，图1-5两刚性杆连接两小球组成的双摆，确定两小 球位置的直角坐标为 它们必须满足下面两个约束方程
可见有两个独立坐标，即质点系有两个自由度。 确定一个质点系位置的独立参数选取一般不是唯一的 ，如上述双摆，可以选中的任意两个作为独立参数，也 可以选取角作为独立参数。我们把这些能完全确定质点系位置的独 可以选取角作为独立参数。我们把这些能完全确定质点系位置的独 立参数称为质点系的广义坐标。显然，广义坐标数目等于确定质点 立参数称为质点系的广义坐标。显然，广义坐标数目等于确定质点 系位置的独立参数数目。在完整约束的情况下 系位置的独立参数数目。在完整约束的情况下，质点系的广义坐标 在完整约束的情况下， 的数目等于自由度数。 的数目等于自由度数。 如果以 表示一非自由质点系的广义坐标，则各质 点的直角坐标都可以写成这些广义坐标的函数。对于完整、双面和 定常约束，可以写成如下的函数形式
第一章 虚位移定理
§1-1 约束及约束方程
在几何静力学中，我们将限制某物体位移的周围物体 称为该物体的约束。现在从运动学角度来看约束的作用 称为该物体的约束。现在从运动学角度来看约束的作用， 现在从运动学角度来看约束的作用， 一非自由质点系的位置或速度受到某些条件的限制， 一非自由质点系的位置或速度受到某些条件的限制，这种 限制条件称为该质点系的约束。 限制条件称为该质点系的约束。 例如，圆球被限制在水平面上做纯滚动，这是约束 表现为限制圆球中心到水平面的距离保持不变；圆球与水 平面接触点的速度在每瞬时都为零。在一般情况下，约束 对质点系运动的限制可以通过质点系各质点的坐标或速度 的数学方程式来表达，这种表达式称为约束方程 的数学方程式来表达，这种表达式称为约束方程。 约束方程。
（2）双面约束和单面约束
如果约束在两个方向斗气限制运动的作 用，则称为双面约束 用，则称为双面约束。如图1-4所示单 双面约束。如图1 摆，小球M用长为的刚性杆铰联于球支座O 摆，小球M用长为的刚性杆铰联于球支座O上，小 球只能在半径为的球面上运动，其约束方程为
如果约束只在一个方向起作用，而在另一方向能松驰或消失， 这种约束称为单面约束 这种约束称为单面约束。上例中将刚性杆换成柔性索，则小球不仅 单面约束。上例中将刚性杆换成柔性索，则小球不仅 能在球面上运动，还可以在球面内运动，其约束方程就为
式中 xA , y A 和 xB , y B 分别为A，B两点的坐标。 设质点系各质点对参考系的位置和速度分别以 ɺ ɺ ɺ r1 , r2 , ⋅ ⋅ ⋅, rn 和 r1 , r2 , ⋅⋅⋅, rn 来表示，则约束方程的一般形式为：
ɺ ɺ ɺ f j (r1 , r2 , ⋅⋅⋅, rn ; r1 , r2 , ⋅⋅⋅, rn ; t ) = 0 (j=1,2, ⋅⋅⋅,s)
写成矢量形式为 这就是用广义坐标表示质点位置的一般表达式，这种方程隐含 了约束条件，这是采用广义坐标的方便之处。
又车轮每一瞬时与轨道接触点C 又车轮每一瞬时与轨道接触点C的 速度均为零，车轮受到运动约束，其 约束方程为 或写成下面形式 若将上式积分，得
由此可见，可积分的运动约束方程，通过积分可以转化 为完整约束方程。可积分的运动约束与完整约束实质上 是等价的。 非完整约束中最简单的是线性非完整约束，它的约束方程中包 含速度的线性项，方程的一般形式为
f j ( x1 , y1 , z1 ,⋅ ⋅ ⋅, xn , yn , zn ; t ) = 0 (j = 1,2,⋅ ⋅ ⋅, s)
式（1 ）和式（1 式（1-1）和式（1-2）表示的均为完整约束。 如果约束方程中包含有坐标对时间的导数，或者说，约束还限 制各质点的速度，这种约束称为非完整约束 运动约束。约束方的 制各质点的速度，这种约束称为非完整约束或运动约束。约束方的 非完整约束或 一般形式为
如图1 所示质点M被限制在半径为R 如图1-1所示质点M被限制在半径为R的球面上运动， 质点的位置由直角坐标（x,y,z）表示，则质点M 质点的位置由直角坐标（x,y,z）表示，则质点M的约束方 程为: 程为:
又如图1 所示Oxy平面内的曲柄连杆机构，曲柄销A 又如图1-2所示Oxy平面内的曲柄连杆机构，曲柄销A 被限制在以O为中心，r为半径的圆周上运动；滑块B 被限制在以O为中心，r为半径的圆周上运动；滑块B被限 制在沿Ox轴的水平直槽中运动；A,B两点间的距离等于. 制在沿Ox轴的水平直槽中运动；A,B两点间的距离等于.此机构的 约束方程可表示为
ɺ ɺ ɺ ɺ ɺ ɺ f j ( x1, y1, z1,⋅ ⋅ ⋅, xn , yn , zn ; x1, y1, z1, ⋅ ⋅⋅, xn , yn , zn ; t ) = 0
这种约束是用微分方程形式表示的，一般来说，是不 可积分但也有些例外的情况，例如图1 所示，半径为r 可积分但也有些例外的情况，例如图1-3所示，半径为r的 车轮沿直线轨道作纯滚动。 车轮轮心A至轨道的距离始终保持不 车轮轮心A 变，所以其几何约束方程为
（3）定常约束和不定常约束 如果约束方程中不显含时间t，这种约束称为定 如果约束方程中不显含时间t，这种约束称为定 常约束或稳定约束。它的约束方程一般形式为 常约束或稳定约束。它的约束方程一般形式为
ɺ ɺ ɺ ɺ ɺ ɺ f j ( x1, y1, z1, ⋅⋅⋅, xn , yn , zn ; x1, y1, z1, ⋅⋅⋅, xn , yn , zn ) = 0
式中n为质点系的质点数，s为约束方程数,⋅⋅⋅,n)
用直角坐标时，可写成
ɺ ɺ ɺ f j ( xi , yi , zi; xi , yi , zi; t) = 0
按约束对质点系运动限制的不同情况，可将约束分类如下：
（1）完整约束和非完整约束 约束方程中不包含坐标对时间的导数，或者说，约 束只限制质点系各质点的几何位置，而不限制其速度，这种约束称 为完整约束或几何约束。其约束方程一般形式为 完整约束或几何约束。其约束方程一般形式为