The vertices of a triangle ABC are given by the coordinates A(3, 2), B(0, 4) and C(5, 3). Triangle ABC is mapped onto triangle A'B'C', the coordinates of its vertices being $\mathrm{A}^{\prime}\left(-3, \frac{9}{2}\right) \mathrm{B}^{\prime}(-6,0)$ and $\mathrm{C}^{\prime}\left(-\frac{9}{2}, \frac{15}{2}\right)$. a) Find the matrix which maps ABC onto A'B'C'. b) Find the matrix which maps A'B'C' onto ABC.

From the list below, supply the words needed to complete the paragraph. Some words will not be used. anachronism, lethal, effusive, gape, holocaust, defunct, embroil. The argument over the reality of global warming _____ many scientists, most of whom disagree among themselves. Some claim that global warming will cause a planetary _____ in which nothing will survive. Other scientists claim such _____ theories are meant only to cause worldwide panic. Indeed, they agree that global warming exists, but that it might take thousands of years to cause the climate to become _____. In a thousand years, or even a hundred years, they assert, the processes that cause global warming will be made _____ by new technologies.

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. The revolutionaries $\mathit{effaced}$ statues of the former dictator because...

Multiply the following matrices: a)

$$\left(\begin{array}{rr}{1} & {-2} \\ {4} & {2} \\ {-5} & {3}\end{array}\right)\left(\begin{array}{rr}{9} & {-1} \\ {3} & {7}\end{array}\right)$$

b)

$$\left(\begin{array}{ccc}{2} & {-3} & {5}\end{array}\right)\left(\begin{array}{rr}{6} & {3} \\ {2} & {1} \\ {-5} & {-7}\end{array}\right)$$

Write two matrices with a determinant of 0.

Complete the sentence in a way that shows you understand the meaning of the italicized vocabulary word. Myra became $\mathit{pensive}$ when Cal told her that she...

In the following, calculate $\mathbf{V} \times \mathbf{W}$ and where possible $\mathbf{W} \times \mathbf{V} .$

$$\mathbf{V}=\left(\begin{array}{rrr}{4} & {6} & {1} \\ {3} & {2} & {-3}\end{array}\right)$$

$$\mathbf{W}=\left(\begin{array}{rr}{2} & {1} \\ {-4} & {-3} \\ {6} & {5}\end{array}\right)$$

Sketch the graphs of the following functions: a) $y=x^{2}$ b) $y=-x^{2}$

Two methods for locating the midpoint of a line segment are using the Midpoint Formula and constructing the bisector of a line segment. How are the two methods different?

Determine all values of a and b for which the augmented matrix has each given number of solutions.

$$\left[\begin{array}{rrrr} {1} & {2} & {\vdots} & {-4} \\ {0} & {a} & {\vdots} & {b} \end{array}\right]$$

(a) Exactly one solution. (b) Infinitely many solutions. (c) No solution.

You are choosing between camping outfitters. Outfitter A charges a reservation fee of $150 plus a daily guide fee of$70. Outfitter B charges a reservation fee of $75 plus a daily guide fee of$90. Estimate when the cost of Outfitter A equals the cost of Outfitter B.

Use the properties of logarithms to expand the expression as a sum, difference, and or multiple of logarithms. (Assume all variables are positive.) $\log _{3}\left(3^{2} \cdot 4^{2}\right)$

Consider an air-standard jet engine cycle operating in a 280-K, 100-kPa environment. The compressor requires a shaft power input of 4000 kW. Air enters the turbine state 3 at 1600 K and 2 MPa, at the rate of 9 kg/s, and the isentropic efficiency of the turbine is 85%. Determine the pressure and temperature entering the nozzle.

What are the common approximations made in the analysis of heat exchangers?