Show that the system

$$\begin{array}{l}{x^{\prime}=y} \\ {y^{\prime}=-\sin x-y}\end{array}$$

has an equilibrium point at the origin. Compute the Jacobian, then discuss the type and stability of the equilibrium point. Find and describe other equilibria if they exist.

Estimate using front-end estimation.

$$14.39 + 79.12$$

Set up (but do not evaluate) the double integral for the surface area of the given portion of surface. -The surface given by $z=x^{2}+3 x y+y^{2}$ over the region in the xy-plane bounded by $0 \leq x \leq 4$, $0 \leq y \leq x$

Complete the sentences. A metric unit of capacity that is equal to one thousandth of a liter is a _________

The following complex voltages are written in a combination of rectangular and polar form. Rewrite each, using conventional phasor notation (i.e., a magnitude and angle): (a) $\dfrac{2-j}{5\angle 45^{\circ}}\;\mathrm{V}$. (b) $\dfrac{6\angle 20^{\circ}}{1000}-j$. (c) $(j) (52.5 \angle -90^{\circ})\;\mathrm{V}$.

Determine whether the statement is true or false. A matrix representation of a linear operator on $M_{m\times n}$ is an $m\times n$ matrix.

Compare. Use > , < , or = to complete each statement.

$$18 - 6 \div 3 \ ? \ ( 18 - 6 ) \div 3$$

Identify two illustrations that add meaning to McCloud's definition of a comic. Explain.

A cop pulls you over and asks what speed you were going. "Well, officer, I cannot tell a lie; the speedometer read $4\times10^8\mathrm{~m/s}$." He gives you a ticket, because the speed limit on this highway is $2.5\times10^8\mathrm{~m/s}$. In court, your lawyer (who, luckily, has studied physics) points out that a car's speedometer measures proper velocity, whereas the speed limit is ordinary velocity. Guilty, or innocent?

Define the sample space.

Two vectors $u$ and $v$ are given. Compute the norms of the vectors and the distance $d$ between them.

$$\begin{equation*} u=\begin{bmatrix}5\\-3\end{bmatrix},\text{ and } v=\begin{bmatrix}2\\4\end{bmatrix} \end{equation*}$$

Apply the shifted inverse power method to the companion matrix C(p) of p to approximate the root of p closest to a to three decimal places.

$$p ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 1 , \alpha = 0$$

If E and F are events with $P( F)=0.38 \text{ and } P(E|F)=0.46,$ find $P(E\cap F).$

Solve the given linear equation. 3x + 4 = 7