Construct the general solution of x'=Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories.

$$A=\left[ \begin{array}{rrr}{-8} & {-12} & {-6} \\ {2} & {1} & {2} \\ {7} & {12} & {5}\end{array}\right]$$

Determine which value best approximates the area of the region bounded by the graph of f (x) = 4 − x2 and the x-axis over the interval [0, 2]. Make your selection on the basis of a sketch of the region, not by performing calculations.

$$\begin{array}{llll}{\text { (a) }-2} & {\text { (b) } 6} & {\text { (c) } 10} & {\text { (d) } 3} & {\text { (e) } 8}\end{array}$$

Consider a bright star in our night sky. Assume its distance from the Earth is 20.0 light-years (ly) and its power output is $4.00 \times 10 ^ { 28 }$ W, about 100 times that of the Sun. Find the intensity of the starlight at the Earth.

Illustrate on a 2 -dimensional grid the sample space for: rolling a die and tossing a coin simultaneously

Do you think Michael has deserved to be punished by God? Give reasons for your opinion.

Solve the inequality $12 > \dfrac{t}{-6}$ and graph the solutions

For any field F, let $f(x)=x n+a n-1+\ldots+a 1 x+a 0 \in F[x]$ If r1, r2, ..., rn are the roots of f (x), and $\mathrm{ri} \in \mathrm{F}$ for all $1 \leq \mathrm{i} \leq n,$ prove that a) – an – i = r1 + r2 + … + rn. b) (–l)n a0 = r1 + r2 … rn.

Use the order of operations to find the value of each expression.

$$-8(-3) - 5(-6)$$

Solve for x: $e^{x}+e^{-x}=3$

How do fruits aid in the dispersal of angiosperms?

Write an equation for the line containing the indicated points. (2, 4) and (3, 5) _____

Find the integral. Check your answer by differentiation. $\int \frac { d x } { 1 + 2 x ^ { 2 } }$

Use the formulas to find the corresponding least-squares line. (-2.1, 3.5), (-1.3, 2.7), (1.5, 1.3), (2.7, -1.5)

The energy needed to vaporize the melted meteorite at its $2600^{\circ} \mathrm{C}$ boiling temperature is closest to (a) $2 \times 10^{13} \mathrm{J}$ (b) $5 \times 10^{14} \mathrm{J}$ (c) $7 \times 10^{14} \mathrm{J}$ (d) $3 \times 10^{15} \mathrm{J}$