Two ice skaters are holding hands at the center of a frozen pond when an argument ensues. Skater A shoves skater $\mathrm{B}$ along a horizontal direction. Identify (e) If $A$ has a mass of $0.900$ times that of $B$, and $B$ begins to move away with a speed of $2.00 \mathrm{~m} / \mathrm{s}$, find the speed of $A$.

Label the following statements as true or false. In each part, V,W, and $Z$ denote vector spaces with ordered (finite) bases $\alpha, \beta,$ and $\gamma$ respectively; $T : V \rightarrow W$ and $U : W \rightarrow Z$ denote linear transformations; and $A$ and $B$ denote matrices. $\\$ (a)$[\cup T]_${\alpha}$^${\gamma}$=[T]_${\alpha}$^${\beta}$[U]_${\beta}$^${\gamma}$ $(b)$[$\mathrm{T}$(v)]_${\beta}$=[$\mathrm{T}$]_${\alpha}$^${\beta}$[v]_${\alpha} for all$v \in V $(c)$[$\mathrm{U}$(w)]_${\beta}$=[$\mathrm{U}$]_${\alpha}$^${\beta}$[w]_${\beta} for all$w \in $\mathrm{W}$ $(d)$[$\operatorname{lv}$]_${\alpha}$=I $(e)$\left[$\mathrm{T}$^{2}\right]_${\alpha}$^${\beta}$=\left([$\mathrm{T}$]_${\alpha}$^${\beta}$\right)^{2} $(e)$\left[$\mathrm{T}$^{2}\right]_${\alpha}$^${\beta}$=\left([$\mathrm{T}$]_${\alpha}$^${\beta}$\right)^{2} $(f)$A^{2}=I$implies that$A=I$or$A=-I $(g)$$\mathrm{T}$=$\mathrm{L}$_{A}$for some matrix$A .$(h)$A^{2}=O$implies that$A=O,$where$O$denotes the zero matrix.$ $(i)$L_{A+B}=L_{A}+L_{B}$.$ $(j) If$A$is square and$A_{i j}=\delta_{i j}$for all$i$and$j,$then$A=I$ .

Reread the chapter Big Idea and the lesson Key Concepts. We: Summarize what you have learned by converting each of the Key Concept questions into a factual answer. Lesson 1 (three Key Concepts) Lesson 2 (two Key Concepts) Lesson 3 (three Key Concepts)

Assign oxidation states to all of the atoms in the following:

b. $\mathrm{BaCrO}_4$

Suppose that there is a monthly meeting at CIA headquarters for all employees. How many handshakes will it take for every employee at the meeting to shake the hand of every other employee at the meeting once?

Complete the table to record your results.

Number of Employees	2	3	4	5	6	7	$n$
Number of Handshakes

Factor a negative number or a GCF with a negative coefficient from the given polynomial. See the discussed example.

$$-3 a^4+9 a^3-3 a^2$$

In this exercise, express each angle in radian measure as a multiple of $\pi$. (Do not use a calculator.)

$$-240^{\circ}$$

Explain the difference between the graphs of polynomial functions with a degree of 3 that have a positive leading coefficient and the graphs of those with a negative leading coefficient.

Convert each angle from degrees to radians. Express each answer as a multiple of $\pi .$ $-60 ^ { \circ }$

If six people meet, and each person shakes every other person’s hand, how many handshakes are there in all?

A 91-kg parent and a 21-kg child meet at the center of an ice rink. They place their hands together and push. (a) Is the force experienced by the child more than, less than, or the same as the force experienced by the parent? (b) Is the acceleration of the child more than, less than, or the same as the acceleration of the parent? Explain.

Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.

$$2 t^2+t$$

Lakes that have been acidified by acid rain can be neutralized by the addition of limestone $\left(\mathrm{CaCO}_3\right)$. How much limestone in kilograms would be required to completely neutralize a $5.2 \times 10^9-\mathrm{L}$ lake containing $5.0 \times 10^{-3} \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{SO}_4$ per liter?

To estimate your average monthly salary, divide your yearly salary by the number of months in a year. Write an equation to determine your yearly salary when your average monthly salary is $4560.