一、选择题-|||-1. sin (20)^circ cos (10)^circ -cos (160)^circ sin (10)^circ =-|||-()-|||-A. -dfrac (sqrt {3)}(2) B. dfrac (sqrt {3)}(2) C. -dfrac (1)(2) D. dfrac (1)(2)-|||-2. (sin )^4(15)^circ -(cos )^4(15)^circ = ()-|||-A. dfrac (1)(2) B. -dfrac (1)(2) C. dfrac (sqrt {3)}(2) D. -dfrac (sqrt {3)}(2)-|||-3. 已知点A在圆 ^2+(y)^2=4 上,-|||-且 angle xOA=dfrac (7)(12)pi , 则点A的横坐标为 ()-|||-A. dfrac (sqrt {2)-sqrt (6)}(2) B. dfrac (sqrt {2)-sqrt (6)}(4) C. dfrac (1-sqrt {3)}(4) D. dfrac (1-sqrt {3)}(2)-|||-4.在 Delta ABC 中, tan A+tan B+sqrt (3)=sqrt (3)tan Atan B, 则C等于-|||-()-|||-A. dfrac (pi )(3) B. dfrac (2pi )(3) C. dfrac (pi )(6) D. dfrac (pi )(4)-|||-.5. 已知 sin (alpha +dfrac (pi )(3))+cos (alpha -dfrac (pi )(2))-|||-=-dfrac (4sqrt {3)}(5), 则 cos (alpha +dfrac (2pi )(3))= ()-|||-A. dfrac (sqrt {5)}(2) B. -dfrac (3)(5) C. dfrac (4)(5) D. dfrac (3)(5)-|||-6.公元前6世纪,古希腊的毕达哥拉斯学派研究过正五边形-|||-和正十边形的作图方法,发现了黄金分割,其比值约为-|||-0.618,这一数值也可以表示为 =2sin (18)^circ , 若 ^2+n=4,-|||-则dfrac (msqrt {n)}(2{cos )^2(27)^circ -1}= (C-|||-A.8 B.4 C.2 D.1-|||-7.设 =cos (50)^circ cos (127)^circ +cos (40)^circ sin (127)^circ , =dfrac (sqrt {2)}(2)(sin (56)^circ --|||-cos56°), =dfrac (1-{tan )^2(39)^circ }(1+{tan )^2(39)^circ } 则a,b,c的大小关系是 ()-|||-A. gt bgt c B. gt agt c C. gt agt b D. gt cgt b-|||-8. 若 sin 2alpha =dfrac (sqrt {5)}(5) sin (beta -alpha )=dfrac (sqrt {10)}(10).-|||-且 alpha in [ dfrac (pi )(4),pi ] beta in [ pi ,dfrac (3pi )(2)] , 则 alpha +beta 的值是(B-|||-A. dfrac (9pi )(4) B. dfrac (7pi )(4) C. dfrac (5pi )(4) 或 dfrac (7pi )(4) D. dfrac (5pi )(4) 或dfrac (9pi )(4)

下列函数为奇函数的是 （ ）A. y=-|x|B. y=2-xC. y=(1)/((x)^3)D. y=-x2+8

求指导本题解题过程，谢谢您！28化二次积分 =(int )_(0)^1dx(int )_(0)^xf(sqrt ({x)^2+(y)^2})dy 为极坐标下的二次积分,则 I= ()-|||-A. (int )_(0)^dfrac (pi {4)}dtheta (int )_(0)^dfrac (1{cos theta )}f(r)rdr B. (int )_(0)^dfrac (pi {4)}dtheta (int )_(0)^dfrac (1{sin theta )}f(r)rdr A-|||-C. (int )_(0)^dfrac (x{4)}dtheta (int )_(0)^dfrac (1{cos theta )}f(r)dr D. (int )_(0)^dfrac (x{4)}dtheta (int )_(0)^dfrac (1{sin theta )}f(r)dr

2(15分)f=overline(x)_(1)x_(1)+3overline(x)_(1)x_(3)+4overline(x)_(2)x_(2)-3overline(x)_(3)x_(1)+overline(x)_(3)x_(3)(1).写出Hermite二次型对应的矩阵;(2).求酉矩阵U，使得二次型变为标准二次型。<|im_end|>(1).写出Hermite二次型对应的矩阵；<|im_end|>(2).求酉矩阵U，使得二次型变为标准二次型.

与十六进制数F1相等的有（）A. A 361OB. B 221DC. C 241DD. D 11110001B

右图中的直线AB是________线，BC是________线，CD是________线。

(1)设系统由100个相互独立的部件组成.运行期间每个部件损坏的概率为0.1.至少有85个部件是完好时系统才能正常工作,求系统正常工作的概率.(Ф()=0.9522) (2)如果上述系统由n个部件组成,至少有80%的部件完好时系统才能正常工作.问n至少多大才能使系统正常工作的概率不小于0.957(Ф(1.645)=0.95)

设函数(x)=cos x+(x)^4，那么 f ' ( 0 ) = ( ) A , 1 B , -1 C , 0 D , 4

若 gt 1, 则 +dfrac (1)(a-1) 的最小值是 () .-|||-A.2 B.a-|||-C. sqrt (dfrac {a)(a-1)} D. 3

4.用初等变换法判定下列矩阵是否可逆,如可逆,求其逆矩阵.-|||-(1) (} 1& 0& 0 1& 2& 0 1& 2& 3 .