Explain the difference between exponential growth and exponential decay.

Prove that for three sets \( \mathrm{A}, \mathrm{B} \) and C . \( (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime} \) \( (A \cup B)^{\prime}=A^{\prime} \cap B^{\prime} \) Define Cartesian nroduct of two sets.

A computer technician charges a fixed amount for a repair, plus an additiona What is the meaning of the initial amount for the equation? A. It means the technician charges \( \$ 45 \) per hour for the repair. B. It means the technician charges a fixed amount of \( \$ 45 \) for the repair. C. It means the technician charges a fixed amount of \( \$ 75 \) for the repair, D. It means the technician charges \( \$ 75 \) per hour for the repair.

1. Find the Eigen values of the matrix \( A=\left[\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & 2\end{array}\right] \)

1. Two of the Eigen values of the matrix \( A=\left[\begin{array}{lll}2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right] \) are equal to 1 each. Then solve the Eigen values of \( A^{-1} \).

2. Вычислить и построить на комплексной плоскости число \( \sqrt[3]{\left(-\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^{2}} \). \( \left(\begin{array}{cc}1 & i \sqrt{3})^{3}\end{array}\right. \)