2023 math

1. 已知集合 \(M=\left\{-2,-1,0,1,2\right\}\) ，\(N=\left\{x\left|x^{2}-x-6\geq0\right.\right\},\)则 \(M\cap N=\)

A.\(\{-2,-1,0,1\}\)
B.\(\{0,1,2\}\)

C.\(\{-2\}\)
D. 2

2.已知 \(z=\frac{1-i}{2+2i}\)，则\(z-\overline{z}=\)

A. -i
B. i
C. 0
D. 1

3.己知向量 \(\vec{a}=(1,1),\vec{b}=(1,-1)\)，若 \(\left(\vec{a}+\lambda\vec{b}\right)\perp\left(\vec{a}+\mu\vec{b}\right)\) 则

A.\(\lambda+\mu=1\)

B.\(\lambda+\mu=-1\)

C.\(\lambda\mu=1\)

D.\(\lambda\mu=-1\)

4.设函数 \(f(x)=2^{x(x-a)}\) 在区间(0,1)上单调递减，则a的取值范围是

A.\((-\infty,-2]\)

B. [-2,0)

C.(0,2]

D.\([2,+)\)

5.设椭圆 \(C_1:{\frac{x^2}{a^2}}+y^2=1(a>1),C_2:{\frac{x^2}{4}}+y^2=1\) 的离心率分别为\(e_1\),\(e_2\),，若 \(e_2=\sqrt{3}e_1,\) 则a=

A.\(\frac{2\sqrt{3}}{3}\)

B.\(\sqrt{2}\)

C. \(\sqrt{3}\)

D. \(\sqrt{6}\)