Find all the characteristic values and vectors of the matrix.

$$\left( \begin{array}{ll}{3} & {4} \\ {5} & {2}\end{array}\right)$$

This essay may include references that are unfamiliar to you. Choose at least one unfamiliar detail, and briefly research it. Then, explain how the information you learned from research sheds light on an aspect of the essay.

Find the general solution of the differential equation

$$y''+y=\dfrac{1}{1+\sin x}$$

How do you prompt the user to enter an input using a dialog box?

How is the shape of this distribution similar to or different from the shape of the distribution for the number of pets?

Write a recursive program to generate random sentences from a given BNF grammar. A BNF grammar is a recursively defined file that defines rules for creating sentences from tokens of text. Rules can be recursively self-similar. The following grammar can generate sentences such as “Fred honored the green wonderful child”:

<s>::=<np> <vp>
<np>::=<dp> <adjp> <n>|<pn>
<dp>::=the|a
<adjp>::=<adj>|<adj> <adjp>
<adj>::=big|fat|green|wonderful|faulty|subliminal|pretent
ious
<n>::=dog|cat|man|university|father|mother|child|televisi
on
<pn>::=John|Jane|Sally|Spot|Fred|Elmo
<vp>::=<tv> <np>|<iv>
<tv>::=hit|honored|kissed|helped
<iv>::=died|collapsed|laughed|wept

What is a client when discussing home networks?

(a) In what state is the washwoman when she arrives at the author's home? (b) What has she endured to get there, and how is that situation more difficult when she leaves? Explain.

Draw a number line like the one in the given figure. Place equally spaced tick marks on your number line so that you can plot $\displaystyle \frac{1}{3}$ on a tick mark without first plotting $1$. Then plot $\displaystyle \frac{1}{3}$. Explain your reasoning.

(a)Why does the speaker compare dreams to pocket handkerchiefs? (b)Do you think this is an effective comparison? Why or why not?

How does Clifton describe Miss Rosie in lines 9-10? (b)What does this description imply about Miss Rosie?

Find $\mathcal L^{-1}\{F(s)\}$ for each of the functions $F$.

$$F(s)=\frac{s+5}{s^{4}+3 s^{3}+2 s^{2}}$$

A candy bowl contains $723$ candies. Some of the candies are red, and the rest are green. There are twice as many green candies as red candies. How many red candies are in the candy bowl? Solve this problem in two ways: with the aid of a diagram and with algebraic equations. Explain both solution methods, and discuss how they are related.

Write a program that constructs a rectangle with area 42 and a rectangle with perimeter 42 . Print the widths and heights of both rectangles.