Simplify the expression.

$$\left( s ^ { 5 } \right) ^ { 2 } \left( s ^ { 3 } \right) ^ { 8 }$$

For the phrase in the first column, write the letter of the synonymous phrase in the second column.

$$\begin{matrix} \text{variety of unnecessary things} & \text{a. dispute en route}\\ & \text{b. untained paint}\\ & \text{c. short report}\\ & \text{d. inane refrain}\\ & \text{e. delicate delegate}\\ & \text{f. enamored stammering}\\ & \text{g. submissive sister}\\ & \text{h. imbue with the blues}\\ & \text{i. extraneous miscellany}\\ & \text{j. underfeed the steed}\\ \end{matrix}$$

For the system

$$\overrightarrow{\textbf{x}}'=\begin{bmatrix}-2&0\\0&-2\end{bmatrix}\overrightarrow{\textbf{x}}$$

(star node), verify that the equilibrium point at the origin has the geometric character claimed, and determine its stability behaviour.

A fly sits on a potter’s wheel 0.30 m from its axle. The wheel’s rotational speed decreases from 4.0 rad/s to 2.0 rad/s in 5.0 s. Determine (a) the wheel’s average rotational acceleration, (b) the angle through which the fly turns during the 5.0 s, and (c) the distance traveled by the fly during that time interval.

Find the slope of the line that passes through each pair of points. (-2, 1), (7, 1)

Find $\int _ { 2 } ^ { 3 } f ( x ) g ^ { \prime } ( x ) d x,$ given that $\int _ { 2 } ^ { 3 } f ^ { \prime } ( x ) g ( x ) d x = 1.3$ and the values in the table:

$$\begin{matrix} x & f(x) & f ^ { \prime } ( x ) & g(x) & g ^ { \prime } ( x ) \\ \text{2} & \text{5} & \text{-1} & \text{0.2} & \text{3}\\ \text{3} & \text{7} & \text{-2} & \text{0.1} & \text{2}\\ \end{matrix}$$

Write the letter of the pair of terms that express the relationship closest to that of the capitalized pair. RENOWN : FAME :: (a) greed : cowardice, (b) courtesy : politeness, (c) friendship : conflict

A 1.00-kg ball having net charge $Q = 5.00 \mu \mathrm { C }$ is thrown out of a window horizontally at a speed v = 20.0 m/s. The window is at a height h = 20.0 m above the ground. A uniform horizontal magnetic field of magnitude B = 0.010 0 T is perpendicular to the plane of the ball’s trajectory. Find the magnitude of the magnetic force acting on the ball just before it hits the ground. Hint: Ignore magnetic forces in finding the ball’s final velocity.

Give the number and type of chromosomes in the karyotype of a human somatic cell. How do the chromosomes of a male and a female differ from each other?

Use the residue theorem to evaluate the integral. $\oint_{\gamma} \frac{\cos (z)}{z e^{z}} d z$ with $\gamma$ the circle of radius 1/2 bout i/8.

A man sits with his back against the back of a chair, and he pushes a block of mass m = 2 kg straight forward on a table in front of him, with a constant force F = 30 N, moving the block a distance d = 0.3 m. The block starts from rest and slides on a low-friction surface. Now suppose that the man is sitting on a train that is moving in a straight line with speed V = 15 m/s, and you are standing on the ground as the train goes by, moving to your right. From your perspective (that is, in your reference frame), answer the following question: Consider the system of the man plus the block: how much work does the chair do on the man, and how does this compare with the work done by the chair in the man's reference frame?

Find the regression equation, letting the first variable be the predictor (x) variable. Find the best predicted temperature at a time when a cricket chirps 3000 times in l minute. What is wrong with this predicted temperature?

$$\begin{array} {|c | c | c | c | c | c | c | c | } \hline \text{Chirps in 1 min}&882 & { 1188 } & { 1104 } & { 864 } & { 1200 } & { 1032 } & { 960 } & { 900 } \\ \hline \text{Temperature (}^\circ F)&69,7 & { 93.3 } & { 84.3 } & { 76.3 } & { 88.6 } & { 82.6 } & { 71.6 } & { 79.6 } \\ \hline \end{array}$$

A drug with concentration 0.16 g/cc is delivered into an organ at the rate of 6 cc/sec and is dispersed at the same rate. Suppose the organ has volume 200 cc and initially contains none of the drug. Set up and solve a differential equation for the amount of drug A(t) in the organ at time t.

Assume that the function has an inverse. Without solving for the inverse, find the indicated function values. $f(x)=\sqrt{x^{3}+2 x+4}$, $f^{-1}(2)$