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.

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

Write a class Polynomial that stores a polynomial such as

$$p(x)=5 x^{10}+9 x^7-x-10$$

as a linked list of terms. A term contains the coefficient and the power of $x$. For example, you would store $p(x)$ as

$$(5,10),(9,7),(-1,1),(-10,0)$$

Supply methods to add, multiply, and print polynomials. Supply a constructor that makes a polynomial from a single term. For example, the polynomial p can be constructed as

Polynomial p = new Polynomial(new Term(-10, 0));
p.add(new Polynomial(new Term(-1, 1)));
p.add(new Polynomial(new Term(9, 7)));
p.add(new Polynomial(new Term(5, 10)));

Then compute $p(x) \times p(x)$

Polynomial q = p.multiply(p);
q.print();

(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.

Given the matrices $A$ and $\mathbf{B},$ find the product $\mathbf{A B}$. Also, find the product $\mathbf{B} \mathbf{A}$ in each case in which it is defined.

$$\mathbf{A}=\left( \begin{array}{rr}{3} & {2} \\ {-1} & {4} \\ {5} & {-2}\end{array}\right), \quad \mathbf{B}=\left( \begin{array}{rrr}{3} & {0} & {2} \\ {-1} & {2} & {-3}\end{array}\right)$$

Given the matrices $A$ and $\mathbf{B},$ find the product $\mathbf{A B}$. Also, find the product $\mathbf{B} \mathbf{A}$ in each case in which it is defined.

$$\mathbf{A}=\left( \begin{array}{rr}{5} & {-2} \\ {4} & {3}\end{array}\right), \quad \mathbf{B}=\left( \begin{array}{rr}{-1} & {8} \\ {2} & {-5}\end{array}\right)$$

Find the general solution of the differential equation

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

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

Describe an O(n)-time algorithm that, given a set S of n distinct numbers and a positive integer k ≤ n, determines the k numbers in S that are closest to the median of S.

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

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

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.

What is a client when discussing home networks?

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

Generalize methods mazeTraversal and mazeGenerator of earlier exercises to process mazes of any width and height.