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关于特征值和特征向量的若干结论

因为矩阵的特征值中有一个0，所以矩阵的行列式的值为0，解得未知数

多做几道

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材料全屏SingaporeSingapore is an independent city-state in southeastern Asia, consisting of one major island—the Singapore island—and more than 50 small islands, located off the southern tip of Malay. The city of Singapore, the capital of the country, is at the southeastern end of the Singapore Island; it is one of the most important port cities and commercial centers of Southeast Asia. The total area of the republic is 640 sq kmLow-lying Singapore Island has no outstanding relief(轮廓鲜明的) features. A central area of hills rises to the maximum height of 176 m. The country has a wet tropical climate, with an average annual temperature of 27.20℃. The average annual rainfall is 2.413 mm. the wettest months are November through January.Singapore is governed under a constitution of 1959. A president, elected to a four-year term, is head of state, and a prime minister is head of government. The president used to be selected by Parliament, but by 1991 constitutional amendment（修正案）, the president is now elected directly by the people. The Parliament is the law-making body with its 81 members popularly elected.In the late 1980s the country had some 290 primary schools with 278,300 pupils and 160 secondary schools with 200,200 students. The main institutions of higher education are the National University of Singapore, several technical colleges, and a teachers college.Singapore has one of the highest standards of living of any country in Asia. In the late 1980s the gross domestic product was estimated at $23.7 billion, or $8, 870 per person. The fishing industry is centered on the port of During, on southwestern Singapore Island. Industry has grown rapidly since the 1960s, and Singapore now produces a diversity of goods, including chemicals, electronic items, clothing, and processed foods, etc. Shipbuilding and petroleum refining are also important.1【单选】Paragraph 1（）AEducationBLand and ClimateCState SystemD General IntroductionEEconomyFPopulation
Paragraph 2（）AEducationB Land and ClimateCState SystemD General IntroductionEEconomyFPopulation
Immigration and ProblemsHundreds of thousands of people supporting immigration rights in the US filled streets all over America in early 2006. Many held signs and American flags and asked to be __1__ as citizens rather than criminals. Senator John McCain held the opinion that the country should open a __2__to citizenship to immigrants(移民) who were already in the country illegally, while other politicians__3__ for stricter measures---including rounding up undocumented immigrants and sending them back to their home countries.Canadian officials say that immigration applications continue to rise. Some want to keep the doors __4__. They need the labor. About 400,000 immigrants were allowed into the country in 2005, according to the Canadian Government statistics. __5__ all this growth means that cities need to adapt. New comers don’t always make a smooth transition into jobs for which they are skilled. So industries are using mentoring(辅导)programs to help new __6__ find proper jobs.With the large numbers of undocumented African immigrants arriving in the Canary Islands, the Spanish Government has decided to get __7__. There will be no more mass amnesties(特赦)for the illegal immigrants, and anyone coming to Spain without __8__ will be sent back.France's new immigration and integration law gives the government new powers to encourage high-skilled migration. It takes __9__ in 2007. The new law authorizes the government to help these identified employers find immigrant workers with needed skills or qualifications. The selected foreign employees will be granted"skills and talents"visas(签证). But some people show the concern that it’ll cause brain drain in 40 countries.A. immigrants B. HoweverC developing D.pathE. open F. toughG. effect H. ThereforeI developed J. permissionK. treated L.called
Testing: Is it the only way to Evaluate Students?About ten percent of __1__ (spend)on primary and secondary education in the United States comes from the federal government. For ten years now, federal law has tied this cost to student __2__ (perform). States have been required to show progress through __3__ (year) testing.States saying testing tells only part of the story about efforts by school and students to improve. So the Obama administration has eased the limits on states in __4__ (measure) performance.The western state of Colorado for example, has a new __5__ (assess) method. The idea is to show __6__ (academy) growth, not just achievement on tests. It combines test scores, family income levels, school size, the ethnicity of the student and many other factors.Josh Smith is principal of a middle school in a network of public charter schools __7__ (call). West Denver Prep Charter schools are publicly funded but not operated the same as __8__ (tradition) public schools. Mr. Smith says he likes to show his students this graph so they can see their school’s progress. On average, students enter sixth grade at West Denver Prep __9__ (perform) below grade level. __10__ (strange) enough, most are outperforming other students across the state three years later.
材料全屏Saving MoneyWhere you save your money often depends on what you are saving for. If you are saving to buy a dictionary or to go to a concert, then you probably keep your money __1__ in your roomIf you are __2__ for a big purchase like a mountain bike or a school trip, where would you save your money?One place to save money is the bank. Putting your money in a savings account will help yourmonev__3__ more money. If you put your money in a piggy bank(猪形储蓄罐), one year later you'll still have the __4__ amount of money you put in. If you put your money in a savings account, one year later, you'll have more money than you put in. Why?When you keep your money in a __5__, your money earns interest. __6__ is the amount of a bank pays you to use your money. The bank uses your money (and the money of other people) to loan money to people and businesses.Another way you can save money is to buy a certificate of deposit or CD. If you have some money that you don't need to use for a __7__ time, this is a good way to make your money __8__.Since the bank is using your money for that time period, it will __9__ you interest. You will earn more interest with a CD than in a savings account. Can you guess why? It's because you promise to leave your money in the bank for a certain period of time. Banks pay __10__ rates of interest.1【简答】A. long B. same C. bank D. earn E. pay F. grow G. inside H. different I. interest J. somewhere K. saving L raise
Cell Phones: Hang Up or Keep Talking?Millions of people are using cell phones today. In many places it is actually considered __1__ (usual) not to use one. They find that the phones are more than a means of __2__ (communicate)---having a mobile phone shows that they are cool and __3__(connect).The __4__ (explode) around the world in mobile phone use make some health professional worried. Some doctors are __5__ (concern) that in the future many people may suffer health problems from the use of mobile phones. In England, there has been a serious debate about this issue. Mobile phone companies are worried about the negative 46(public) of such ideas. They say that there is no __7__ (prove) that mobile phones are bad for your health.On the other hand, signs of change in the issues of the brain and head can be __8__ (detect) with modern scanning equipment. What is it that makes mobile phones __9__ (potential) harmful? The answer is radiation.As the discussion about their safety continues, it appears that it's best to use mobile phones less often. Use your regular phone if you want to talk for a long time. Use your mobile phone only when you really need it. Mobile phones can be very useful and convenient, especially in emergencies. In the future, mobile phones may have a __10__ (warn) label that says they are bad for your health. So for now, it's wise not to use your mobile phone too often.
材料全屏 Job or Money【*】Would you quit your job if you didn't need the money? In a 1990 poll by the Gallop Organization, many people said quitting work was an important reason to be rich. Yet researchers find that work is one of life's chief satisfactions for people.Consider W. Berry Fowler. In 1979, Fowler started a tutoring company that became so successful he was able to sell out and retire in 1978a multimillionaire at 40. He bought a 50-foot cabin cruiser and a house in Hawaii, and busied himself vacationing.But after five years of perpetual vacation, Fowler began to miss the challenges of work. So in 1992, he bought a fitness chain for children and now spends 75 hours a week immersed in balance sheets and staff meetings."My best days on the golf course weren't half as much fun as a good day at the office, he says.A job, studies show, is more than a paycheck. Doing something well can increase confidence and self-worth. When sociologist H. Ray Kaplan surveyed 139 lottery millionaires, he discovered 60 percent continued working at least a year after they’d won.If jobs are so important, wouldn't salary size be a gauge of job satisfaction? Americans think so. A survey conducted last year by Roper Starch Worldwide, Inc. , found that almost 70 percent of the respondents said they would be happier if their families had twice as much household income. Yet studies show that job satisfaction comes less from how much people earn than from the challenge of their jobs and the control they are able to exert. Work that doesn't engage a person will never seem rewarding, no matter how lucrative it becomes.1【单选】The Gallop poll shows many people want to be rich in order not to work.（）A RightBWrongCNot mentioned
Researchers did another survey after the Gallop poll.（）ARightBWrongCNot mentioned
材料全屏 Moderate Earthquake Strikes England【*】A moderate earthquake struck parts of southeast England on 28 April 2007, toppling chimneys from houses and rousing residents from their beds. Several thousand people were left without power in Kent County. One woman suffered minor head and neck injuries.【*】It felt as if the whole house was being slid across like a fun-fair ride,"said the woman.The British Geological Survey said the 4.3-magnitude(震级)quake struck at 8:19 a.m. and was centered under the English Channel, about 8.5 miles south of Dover and near the entrance to the Channel Tunnel.【*】Witnesses said cracks appeared in and chimneys collapsed across the county. Residents said the tremor had lasted for about 10 to 15 seconds.【*】I was lying in bed and it felt as if someone had just got up from bed next to me,"said Hendrick Van Eck, 27, of Canterbury about 60 miles southeast of London."I then heard the sound of cracking and it was getting heavier and heavier. It felt as if someone was at the end of my bed hopping up and down."There are thousands of moderate quakes on this scale around the world each year, but they are rare in Britain. The April 28 quake was the strongest in Britain since 2002 when a 4. 8-magnitude quake struck the central England city of Birmingham.【*】The country's strongest earthquake took place in the North Sea in 1931, measuring 6.1 on the Richter(里氏)scale. British Geological Survey scientist Roger Musson said the quake took place on 28 April in an area that had seen several of the biggest earthquakes ever to strike Britain, including one in 1580 that caused damage in London and was felt in France. Musson predicted that it was only a matter of time before another earthquake struck this part of England. However, people should not scared too much by this prediction, Musson said, as the modern earthquake warning system of Britain should be able to detect a forthcoming quake and announce it several hours before it takes place. This would allow time for people to evacuate and reduce damage to the minimum.1【单选】During the April 28 earthquake, whole England was left without power.（）ATrueBFalseC Not Given
The 4. 3-magnitude quake struck at 8: 19 p. m. in England and was centered under the English Channel.（）ATrueBFalseCNot Given

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