Use the following matrices. $$ A=\left[\begin{array}13&1\\-1&0\end{array}\right] $$ $$ B=\left[\begin{array}14&2\end{array}\right] $$ $$ C=\left[\begin{array}10\\-2\end{array}\right] $$ $$ D=\left[\begin{array}15&0\\1&2-\end{array}\right] $$ For each part, either do the calculation or explain why it does not make sense. a. $3D$ b. $A+B$ c. $A-D$ d. $B\cdot C$ e. $A\cdot C$ f. $AB$ g. $AC$ h. $AD$

If

$$\overrightarrow{\mathrm{AB}}=\left( \begin{array}{c}{-1} \\ {3} \\ {2}\end{array}\right), \overrightarrow{\mathrm{AC}}=\left( \begin{array}{c}{2} \\ {-1} \\ {4}\end{array}\right) \quad \text { and } \quad \overrightarrow{\mathrm{BD}}=\left( \begin{array}{c}{0} \\ {2} \\ {-3}\end{array}\right)$$

find: a. $\overrightarrow{\mathrm{AD}}$ b. $\overrightarrow{\mathrm{CB}}$ c. $\overrightarrow{\mathrm{CD}}$

In the steel bars $BE$ and $AD$ each have a $6 \times 18-\mathrm{mm}$ cross section. Knowing that $E=200 \mathrm{~GPa}$, determine the deflections of points $A,B$, and $C$ of the rigid bar $ABC$., the $3.2-\mathrm{kN}$ force caused point $C$ to deflect to the right. Using $\alpha=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, determine (a) the overall change in temperature that causes point $C$ to return to its original position, (b) the corresponding total deflection of points $A$ and $B$.

Les étudiants suivants sont $\`{a}$ la biblioth$\`{e}$que. Dites ce que chacun lit et ce que chacun écrit.

1. nous (un magazine de sport / des lettres)

2. Antoine (un livre d'histoire / des notes) $\quad$

3. Fran$\c{c}$oise et Ad$\`{e}$le (un article scientifique / un po$\`{e}$me)

4. toi (une lettre / une carte postale $\`{a}$ Jacques)

5. vous (un livre de fran$\c{c}$ais / un résumé [summary])

6. moi (une carte postale / une lettre $\`{a}$ Sylvie)

7. Annie (un mail / une réponse)

The diagram shows a cuboid ABCDEFGH. The vertex F is located at the origin of a plane and the vertex C has coordinates $(8,10,6)$. The faces of the cuboid are parallel to the coordinate planes.

a. Show that the length of the diagonal of the cuboid is $10 \sqrt{2} \mathrm{~cm}$.

b. Determine the coordinates of the midpoint M of the segment AD.

c. Find the distance between the points F and M

d. Find the perimeter of the triangle CFM, giving your answer exactly.

e. Show that cosine of the angle AMF is equal to $\frac{\sqrt{10}}{10}$.

Rewrite the following sentences, adding, deleting, or changing periods, question marks, exclamation points, and commas as necessary.

EXAMPLE: My best friend has moved to 9782 , Revere Avenue, New York NY 10465-2879

My best frieñ has moved to 9782 Revere Avenue, New York, NY 10465-2879.

Using hyperbole the store claimed in a colorful full-page newspaper ad that it would be having the "World's Most Spectacular Labor Day Sale."

$$\begin{aligned} &\text { Match the following word elements with the definitions. }\\ &\begin{array}{llll} \text { Combining Forms } & \text { } & \text { Suffixes } & \text { Prefixes } \\ \text { caud/o } & \text { kary/o } & \text {-genesis } & \text { ad- } \\ \text { dist/o } & \text { leuk/o } & \text {-gnosis } & \text { infra- } \\ \text { dors/o } & \text { morph/o } & \text {-graphy } & \text { ultra- } \\ \text { eti/o } & \text { poli/o } & & \\ \text { hist/o } & \text { somat/o } & & \\ \text { idi/o } & \text { viscer/o } & & \\ \text { jaund/o } & \text { xer/o } & & \end{array} \end{aligned}$$

far, farthest _________.

The table refers to a survey of senior high school students in Dayton, Ohio. It cross-tabulates whether a student had ever smoked cigarettes and whether a student h ad ever drunk alcohol and shows counts and the conditional distributions of alcohol use.

Find the odds of having used alcohol for users and non- users of cigarettes. Interpret each. Then, describe the strength of association, using the odds ratio.

Following is an excerpt from a five-page ad by WeissneggerForGov.org in The Martian Enquirer criticizing Supreme Martian Administrator, Gov. Red Davis: On Worker Accommodation: Gov. Red Davis: “The median size of Government worker habitats in Valles Marineris is at least 400 square feet.” Weissnegger: “The average size of a Government worker habitat in Valles Marineris is a mere 150 square feet.” The statements attributed to Weissnegger do not contradict the statement attributed to Gov. Davis, right? Explain.

Calculate the given quantity, if it is defined, using the given matrices:

$$\begin{aligned} &A=\left[\begin{array}{ll} {1} & {0} \\ {1} & {9} \end{array}\right] \quad B=\left[\begin{array}{ll} {1} & {1} \\ {1} & {9} \\ {0} & {9} \end{array}\right]\\ &C=\left[\begin{array}{ll} {1} & {2} \\ {9} & {2} \end{array}\right] \quad D=\left[\begin{array}{lll} {1} & {1} & {7} \\ {0} & {3} & {2} \end{array}\right] \end{aligned}$$

AD

Let G be the set of 2 x 2 real matrices

$$\begin{bmatrix} a & b\\ c& d\end{bmatrix}$$

with $ad-bc\neq 0$. Prove that G, together with the operation of matrix multiplication, is a group. Note that the set of all 2 x 2 real matrices do not form a group because some matrices such as

$$\begin{bmatrix}1& 1 \\ 1 & 1\end{bmatrix}$$

, are not invertible. We discard the noninvertible matrices, and what remains is a group. This is analogous to our transformation from $\mathbb{Z}_n$ to $\mathbb{Z}_n^*$.

Recognize and pronounce medical terms pertaining to the body.

a. If a physician tells you to put the patient in the $supine$ position, what should you do?

$$\quad\rule{10cm}{0.15mm}$$

b. If the physician tells you she wants x-rays of the abdominopelvic cavity, what parts of the body would you be looking at?

$$\quad\rule{10cm}{0.15mm}$$

c. What is the correct pronunciation of $abdominopelvic$?

a. ad-domino-PELV-ic

b. ab-DOM-in-no-PEL-vik

c. ab-domino-PELV-ik

d. ab-DOM-ih-no-PEL-vik

Consider the generating functions

$$\begin{array}{ll} A=1+x+x^2, & B=1+2 x+4 x^4+x^5, \\ C=1-x^2+x^4, & D=1+x+x^2+x^3+\cdots, \\ E=1+x^3+x^6+x^9+\cdots, & F=1-x+x^2-x^3+x^4-\cdots . \end{array}$$

In exercise given below, write each indicated expression in the form

$$a_0+a_1 x+a_2 x^2+a_3 x^3+\cdots .$$

If the expression is a polynomial, then compute it completely; otherwise compute it through the $x^7$ term.

AD

$$\begin{aligned} &\text { Match the following word elements with the definitions. }\\ &\begin{array}{llll} \text { Combining Forms } & \text { } & \text { Suffixes } & \text { Prefixes } \\ \text { caud/o } & \text { kary/o } & \text {-genesis } & \text { ad- } \\ \text { dist/o } & \text { leuk/o } & \text {-gnosis } & \text { infra- } \\ \text { dors/o } & \text { morph/o } & \text {-graphy } & \text { ultra- } \\ \text { eti/o } & \text { poli/o } & & \\ \text { hist/o } & \text { somat/o } & & \\ \text { idi/o } & \text { viscer/o } & & \\ \text { jaund/o } & \text { xer/o } & & \end{array} \end{aligned}$$

tail _________.