Perform the elementary row operation or sequence of row operations on A and then produce a matrix $\Omega$ so that $\Omega A$ is the end result.

$$A=\left(\begin{array}{ccc} -4 & 6 & -3 \\ 12 & 4 & -4 \\ 1 & 3 & 0 \end{array}\right)$$

; interchange rows 2 and 3, then add the negative of row 1 to row 2.

Let

$$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$$

be an equation of a conic section in an $xy$-coordinate system. Let $A^\prime x{^\prime}^2+B^\prime x{^\prime}y{^\prime}+C{^\prime}y{^\prime}^2+D{^\prime}x{^\prime}+E{^\prime}y{^\prime}+F{^\prime}=0$ be the equation of the conic section in the rotated $x{^\prime}y{^\prime}$-coordinate system. Use the coefficients $A{^\prime}, B{^\prime}$, and $C{^\prime}$, shown in the equation with the voice balloon pointing to $B{^\prime}$, to prove the following relationships.

$$A{^\prime}+C{^\prime}=A+C$$

A dime has a diameter of 17.91 mm.

a. You place 15 dimes in a row. What is the length of your row of dimes?

b. Write an expression to describe what happens to the length of your row of dimes when you remove x dimes.

How much must you deposit each year into your retirement account starting now and continuing through year 9, if you want to be able to withdraw $80,000 per year forever, beginning 30 years from now? Assume the account earns interest at (a) the generous rate of 10% per year, and (b) a more conservative rate of 4% per year. Compare the two amounts.

Heather and Cindy are playing "Guess My Shape." Heather has to describe a shape to Cindy accurately enough so that Cindy can draw it without ever seeing the shape. Heather gives Cindy these clues: Clue #1: The shape is similar to a rectangle with a base of 7 cm and a height of 4 cm. Clue #2: The shape is five times larger than the shape it is similar to. a. Has Heather given Cindy enough information to draw the shape? If so, sketch the shape on your paper. If not, write a question to ask Heather to get the additional information you need. b. Use what you know about similar shapes to write a set of "Guess My Shape" clues to describe each of the mystery shapes below. Your clues should be complete enough for someone in another class to be able to read them and draw the shape. Be sure to include at least one clue about the relationship between the mystery shape and a similar shape.

Which of the following is an effect of longshore drift?

A Deep deposits of loess are formed.

B A meander forms in a river.

C A delta builds up at a river's mouth.

D Beach sand moves along a coastline.

An operations manager wants to examine the effect of air-jet pressure (in pounds per square inch [psi]) on the breaking strength of the yarn. Three different levels of air-jet pressure are to be considered: 30 psi, 40 psi, and 50 psi. A random sample of 18 yarns are selected from the same batch, and the yarns are randomly assigned, 6 each, to the 3 levels of air-jet pressure. The breaking strength scores are stored in Yam. At the $0.05$ level of significance, is there evidence of a difference among mean breaking strengths for the three air-jet pressures?

A random sample of size $n=81$ is taken from an infinite population with the mean $\mu=128$ and the standard deviation $\sigma=6.3$. With what probability can we assert that the value we obtain for $\bar{X}$ will not fall between $126.6$ and $129.4$ if we use (a) Chebyshev's theorem; (b) the central limit theorem?

Using Semicolons Correctly. In each sentence a command is used instead of a semicolon. Circle the comma to show that a semicolon is needed. The tulips, which looked so beautiful this spring. were planted only last fall, however, we will have to move them when we build the new garage.

Dues water boil at higher temperatures at higher pressures? Explain.

Select the graph that represents the presentation of the solution set.

$$4x-2<10.$$

Given the force field F, find the work required to move an object on the given oriented curve. $\mathbf { F } = \langle y , - x \rangle$ on the path consisting of the line segment from (1, 2) to (0, 0) followed by the line segment from (0, 0) to (0, 4)

For the pair of functions given, state which function increases faster for $x>1$, then use the INTERSECT command of a graphing calculator to find where (a) $f(x)=g(x)$, (b) $f(x)>g(x)$, and (c) $f(x)<g(x)$. $f(x)=x^2, g(x)=x^3$

Find the measures of the indicated angles and arcs. Where marked, C is the center of the circle.