题目内容
设向量α=(a1，a2，…，an)T，β=(b1，b2，…，bn)T都是非零向量，且满足条件αTβ=0．记n阶矩阵A=αβT．求： (1) A2; (2) 矩阵A的特征值和特征向量．
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Many students find the experience of attending university lectures to be a confusing and frustrating experience. The lecturer speaks for one or two hours, perhaps (61) the talk with slides, writing up important information on the blackboard, (62) reading material and giving out (63) The new student sees the other students continuously writing on notebooks and (64) what to write. Very often the student leaves the lecture (65) notes which do not catch the main points and (66) become hard even for the students to understand. Most institutions provide courses which (67) new students to develop the skills they need to be (68) listeners and note-takers. (69) these are unavailable, there are many useful study-skills guides which (70) learners to practice these skills independently. In all cases it is important to (71) the problem before actually starting your studies. It is important to (72) that most students have difficulty in acquiring the language skills (73) in college study. One way of (74) these difficulties is to attend the language and study-skills classes which most institutions provide throughout the (75) year. Another basic strategy is to find a study partner with whom it is possible to identify difficulties, exchange ideas and provide support.
【说明】 以下是客户机/服务器模型中的一个简单的客户机程序(服务器程序略)，其工作过程非常简单：客户机与服务器建立连接后，接收服务器向客户机返回的一条消息。 程序中用到了两种结构hostent与sockaddr_in: hostent类型的结构定义 struct hostent { char*h_name; //主机名称 char**h_aliases; //别名列表 int h_addrtype; //主机地址类型: AF_XXX int H_length; //主机地址长度: 32位 char**h_addr_list; //主机IP地址列表 } #define h_addr h_addr_list[0] sockaddr_in类型的结构定义，sockaddr_in是通用套接字结构sockaddr在TCP/IP协议下的结构重定义，为TCP/IP套接字地址结构。 Struct sockaddrin { short int sin_family;//地址类型AF_XXX，其中AF_INET为TCP/IP专用 unsigned short int sin_port; //端口号 struct in_addrsin_addr; //Internet地址 //端口号以及Internet地址使用的是网络字节顺序，需要通过函数htons转换 } struct iN_addr { _u32 s_addr; //类型为unsignel_long } 程序中使用到了多个函数： struct hostent * gethostbyname( const char*hostname ); 函数gethostbyname查询指定的域名地址对应的IP地址，返回一个hostent结构的指针，如果不成功返回NULL。 int_socket(int domain, int_type, int protocol); 函数socket创建一个套接字描述符，如果失败返回-1。domain为地址类型，type为套接字类型，本题中为SOCK_STREAM; protocol指定协议，本题中为0。 int connect( int sockfd, struct sockaddr*servaddr, int addrlen); 函数connect与服务器建立一个连接，成功返回0，失败返回-1。servaddr为远程服务器的套接字地址，包括服务器的IP地址和端口号；addrlen为地址的长度。 int read( int fd, char*buf, int len); int write( int fd, char*buf, int len); 函数read和write从套接字读和写数据，成功返回数据量大小，否则返回-1。buf指定数据缓冲区，len指定接收或发送的数据量大小。 【socket程序】 #define PORT4490 //定义端口号为4490 int main( int argc, char*argv[ ]) { int sockfd, nbytes; //套接字描述符、读入缓冲区的字节数 char buf[1024]; //缓冲区 stmct hostent*he; //主机信息类型 struct sockaddr_in srvaddr; //Internet套接字结构 if (1) {perror("调用参数为零，请输入服务器的主机名!\n");exit(1); } if (2) {perror("无法通过主机名获得主机信息!\n");exit(1); } if (3) {perror("无法创建套按字!\n");exit(1); } bzero( &srvaddr, sizeof(srvaddr));//置空srvaddr srvaddr, sin_family=AF_INET; srvaddr, sin_port: (4); srvaddr.sin_addr: (5); if(connect(sockfd, (6), sizeof( struct sockaddr))=-1) {perror("连接失败!\n");exit(1); } //连接服务器，如果失败则提示用户 if(( nbytes=read ( sockfd, buf, MAXDATASIZE))=-1) {perror("读失败!\n");exit(1); } //从套容接字中读出数据 buf[nbytes]=’\0’; prinff("读到的内容：%s", buf); close( sockfd); //打印数据并关闭套接字 }
Passage Two Our brains could be hard-wired to be male or female long before we begin to grow testes(丸)or ovaries(卵巢)in the womb. This discovery might explain why some people feel trapped in a body that’s the wrong sex, and could also lead to tests that reveal the true "brain sex" of babies born with ambiguous genitalia(生殖器). Till now, the orthodoxy among developmental biologists has been that embryos develop ovaries and become female unless a gene called SRY on the Y chromosome is switched on. If this gene is active, it makes testes develop instead. This switch is seen as the key event in determining whether a baby is a girl or a boy. Only after the gonads(性腺) form and flood the body with the appropriate hormones, the theory goes, is the sex of our minds and bodies determined. But in a study of mice, a team at the University of California, Los Angeles, has now found that males and females show differences in the expression of no fewer than 50 genes well before SRY switches on. "It’s the first discovery of genes differentially expressed in the brain, "says Eric Vilain, who led the UCLA team. "They may have an impact on the hard-wired development of the brain in terms of sexual differentiation independent of gonadal induction." Vilain is presenting details of seven of the 50 genes to the annual meeting of the American Society of Human Genetics in Baltimore this week. Three of these genes are dominant in females and four are dominant in males. The next step for Vilain and his team will be to show that the genes in question really do influence brain sexuality—and not just in mice. This is likely to be a much tougher proposition than merely showing there are differences in expression. But if the findings are confirmed, they could one day yield blood tests that allow doctors to establish the brain sex of babies born with genitalia that share features of both sexes. At present doctors and parents have to guess which gender to assign for surgical "correction". From paragraph 4 we know that Vilain and his team are going to ______.
Passage One For more than thirty years after astronauts first set foot on the Moon, scientists have been unable to unravel the mystery of where the Earth’s only satellite came from. But now there is direct evidence that the Moon was born after a giant collision between the young Earth and another planet. Previous studies of rocks from the Earth and the Moon have been unable to distinguish between the two, suggesting that they formed from the same material. But this still left room for a number of theories explaining how—for example, that the Moon and Earth formed from the same material at the same time. It was even suggested that the early Earth spun so fast it formed a bulge that eventually broke off to form the Moon. Franck Poitrasson, and his colleagues at the Swiss Federal Institute of Technology have compared Moon rocks with rocks from Earth and discovered a surprising difference. They analysed the weight of the elements present in the rock using a highly accurate form of mass spectroscopy(光谱研究) that involves vaporising a sample by passing it through an argon (氩) flame. Although they appeared very similar in most respects, the Moon rocks had a higher ratio of iron-57 to iron-54 isotopes(同位素)than the Earth rocks. "The only way we could explain this difference is that the Moon and the Earth were partly vaporised during their formation," says Poitrasson. Only the popular "giant planetary impact" theory could generate the temperatures of more than 1700℃ needed to vaporise iron. In this scenario, a Mars-sized planet known as Theia crashed into Earth 50 million years after the birth of the Solar System. This catastrophic collision would have released 100 million times more energy than the impact believed to have wiped out the dinosaurs—enough to melt and vaporise a large portion of the Earth and completely destroy Theia. The debris from the collision would have been thrown into orbit around the Earth and eventually coalesced to form the Moon. When iron is vaporised, the lighter isotopes burn off first. And since the ejected debris that became the Moon would have been more thoroughly vaporised, it would have lost a greater proportion of its lighter iron isotopes than Earth did. This would explain the different ratios that Poitrasson has found. The passage tells us that the Theia crashed into the Earth ______.
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