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

tissue _________.

A. Look at the picture below of Universidad Troyana. Based on the picture, circle the activities in the bank that people do there.

$$\begin{array}{|llll|} \hline \text { leer } & \text { estudiar } & \text { repetir } & \text { dormir } \\ \text { bailar } & \text { almorzar } & \text { pedir } & \text { poder } \\ \text { jugar } & \text { esquiar } & \text { servir } & \text { cocinar } \\ \hline \end{array}$$

B. Now, using the verbs above, complete the ad below that some students are writing to attract people to the Universidad Troyana. ¡La Universidad Troyana es la mejor! Aquí, nosotros... $\cdot$ _____ $\cdot$ _____ $\cdot$ _____ $\cdot$ _____. Para aprender más sobre nuestra universidad, lee lo que dice una de nuestras estudiantes: "¡Hola! Yo soy Catalina, una estudiante de primer año aquí en la Universidad Troyana. Me encanta la vida aquí. Todos los días yo.... $\cdot$ _____ $\cdot$ _____ $\cdot$ _____ $\cdot$ _____. Realmente es la mejor universidad."

Diogenes statim ad armarium contendit. in armadio erant quinque fustes, quod Diogenes extraxit et nobis tradidit. Diogenes immediately hurried to the closet. In the closet there were five clubs, which Diogenes drew out and gave to us. Diogenes had prepared for an eventual attack by stacking his closet with weapons. To be prepared for battle means to expect a battle. The situation could not have been good and peaceful in their part of town. Diogenes was expecting an attack, sooner or later.

Calculate the quantities required in the problem, where

$$\begin{aligned} &\mathbf{A}=\left[\begin{array}{rrr} {-1} & {0} & {3} \\ {2} & {1} & {2} \\ {-1} & {0} & {1} \end{array}\right], \quad \mathbf{B}=\left[\begin{array}{lll} {1} & {3} & {0} \\ {0} & {1} & {0} \\ {0} & {0} & {1} \end{array}\right]\\ &\mathbf{C}=\left[\begin{array}{ll} {1} & {0} \\ {2} & {1} \\ {1} & {3} \end{array}\right], \quad \text { and } \quad \mathbf{D}=\left[\begin{array}{rrr} {3} & {-1} & {0} \\ {2} & {1} & {2} \end{array}\right] \end{aligned}$$

or explain why they are undefined. AD

Trapezoid $ABCD$ is shown. A diagonal is drawn from point $B$ to point $D$. Sides $BC$ and $AD$ are parallel. Sides $BA$ and $CD$ are congruent. Angle $CBD$ is $24$ degrees and angle $BAD$ is $116$ degrees. What is the measure of angle $ABD$ in trapezoid $ABCD$?

A) $24\degree$; B) $40\degree$; C) $64\degree$; D) $92\degree$.

On a computer with word size w, multiplication modulo n where $n < w/2$ can be performed as outlined. Let $T=[\sqrt{n}+1 / 2],$ and $t=T^{2}-n$. For each computation, show that all the required computer arithmetic can be done without exceeding the word size. (This method was described by Head [He80]). a) Show that $0<t \leq T$. b) Show that if x and y are nonnegative integers less than n, then $x=aT+b, y=cT+d$, where a, b, c, and d are integers such that $0 \leq a \leq T, 0 \leq b<T, 0 \leq c \leq T,$ and $0 \leq d<T$. c) Let $z = ad + bc$ (mod n), such that $0 \leq z<n$. Show that $x y \equiv a c t+z T+b d(\bmod n)$. d) Let $a c=e T+f$, where e and f are integers with $0 \leq e \leq T$ and $0 \leq f<T .$ Show that $x y \equiv(z+e t) T+f t+b d(\bmod n)$. e) Let $v \equiv z+e t(\bmod n)$, such that $0 \leq v<n$. Show that we can write $v=g T+h$, where g and h are integers with $0 \leq g \leq T, 0 \leq h<T$, and such that $x y \equiv h T+(f+g) t+b d(\bmod n)$. f ) Show that the right-hand side of the congruence of part (e) can be computed without exceeding the word size, by first finding j such that $j \equiv(f+g) t(\bmod n)$ and $0 \leq j<n,$ and then finding k such that $k \equiv j+b d(\bmod n)$ and $0 \leq k<n,$ so that $x y \equiv h T+k(\bmod n).$ This gives the desired result.

Ptolemy, who lived in the city of Alexandria in Egypt during the second century AD, gave the measured values in the following table for the angle of incidence $\theta_{1}$ and the angle of refraction $\theta_{2}$ for a light beam passing from air into water. Do these values agree with Snell’s Law? If so, what index of refraction results? (These data are of interest as the oldest recorded physical measurements.)

$$\begin{array}{|cc}\hline \theta_{1} & {\theta_{2}} \\ \hline 10^{\circ} & {8^{\circ}} \\ {20^{\circ}} & {15^{\circ} 30^{\prime}} \\ {30^{\circ}} & {22^{\circ} 30^{\prime}} \\ {40^{\circ}} & {29^{\circ} 0^{\prime}} \\ \hline \end{array} \begin{array}{cc|}\hline{\theta_{1}} & {\theta_{2}} \\ \hline 50^{\circ} & {35^{\circ} 0^{\prime}} \\ {60^{\circ}} & {40^{\circ} 30^{\prime}} \\ {70^{\circ}} & {45^{\circ} 30^{\prime}} \\ {80^{\circ}} & {50^{\circ} 0^{\prime}} \\ \hline \end{array}$$

Quadrilateral ABCD is formed by these lines: (AB) is

$$\left(\begin{array}{l}{x} \\ {y}\end{array}\right)=\left(\begin{array}{l}{2} \\ {5}\end{array}\right)+r\left(\begin{array}{l}{4} \\ {1}\end{array}\right)$$

, (BC) is

$$\left(\begin{array}{l}{x} \\ {y}\end{array}\right)=\left(\begin{array}{c}{18} \\ {9}\end{array}\right)+s\left(\begin{array}{c}{-8} \\ {32}\end{array}\right)$$

, (CD) is

$$\left(\begin{array}{l}{x} \\ {y}\end{array}\right)=\left(\begin{array}{c}{14} \\ {25}\end{array}\right)+t\left(\begin{array}{c}{-8} \\ {-2}\end{array}\right)$$

, and (AD) is

$$\left(\begin{array}{l}{x} \\ {y}\end{array}\right)=\left(\begin{array}{l}{3} \\ {1}\end{array}\right)+u\left(\begin{array}{c}{-3} \\ {12}\end{array}\right)$$

, where r, s, t, and u are scalars. Write down vectors $\overrightarrow{\mathrm{AC}}$ and $\overrightarrow{\mathrm{DB}}$ and hence find: (i) $|\overrightarrow{\mathrm{AC}}|$ (ii) $|\overrightarrow{\mathrm{DB}}|$ (iii) $\overrightarrow{\mathrm{AC}} \cdot \overrightarrow{\mathrm{DB}}$

For A = {(-4, -20), (-3, -9), (-2, -4), (-1, -11), (-1, -3), (1, 2), (1, 5), (2, 10), (2, 14), (3, 6), (4, 8), (4, 12)}, define the relation $\mathscr{R}$ on A by (a, b) $\mathscr{R}$ (c, d) if ad = bc. a) Verify that $\mathscr{R}$ is an equivalence relation on A. b) Find the equivalence classes [(2, 14)], [(–3, –9)], and [(4, 8)]. c) How many cells are there in the partition of A induced by $\mathscr{R}?$

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

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. $AD$

Let

$$A = \left[ \begin{array} { r r r } { 1 } & { - 1 } & { 2 } \\ { 3 } & { 1 } & { 4 } \end{array} \right] , B = \left[ \begin{array} { r r r } { 2 } & { - 1 } & { 3 } \\ { 5 } & { 1 } & { 2 } \\ { 4 } & { 6 } & { - 2 } \end{array} \right], \\C = \left[ \begin{array} { r } { 1 } \\ { - 1 } \\ { 2 } \end{array} \right] , D = \left[ \begin{array} { l l l } { 2 } & { - 2 } & { 3 } \end{array} \right], \\E = \left[ \begin{array} { c c } { 2 - i } & { 1 + i } \\ { - i } & { 2 + 4 i } \end{array} \right] , F = \left[ \begin{array} { c c } { i } & { 1 - 3 i } \\ { 0 } & { 4 + i } \end{array} \right].$$

In these problems, i denote

$$\sqrt { - 1 }.$$

For each item, decide whether or not the given expression is defined. For each item that is defined, compute the result. (a) AC, (b) DC, (c) DB, (d) AD, (e) EF

$$( { \mathrm f } ) A ^ { T } B, ( \mathrm { g } ) C ^ { 2 } , ( { h } ) E ^ { 2 },\text { (i) } A D ^ { T },\text { (j) } E ^ { T } A$$

Seven factors are varied at two levels in an experiment involving only 16 trials. A $\frac{1}{8}$ fraction of a $2^7$ factorial experiment is used, with the defining contrasts being ACD, BEF, and CEG. The data are as follows:

$$\begin{matrix} \text{Treat. Comb. } & \text{ Response } & \text{Treat. Comb. } & \text{ Response }\\ \text{(1)} & \text{31.6} & \text{acg} & \text{31.1}\\ \text{ad} & \text{28.7 } & \text{cdg} & \text{32.0 }\\ \text{abce} & \text{33.1 } & \text{beg} & \text{32.8 }\\ \text{cdef} & \text{33.6 } & \text{adefg} & \text{35.3 }\\ \text{acef} & \text{33.7 } & \text{efg} & \text{32.4 }\\ \text{bcde} & \text{34.2 } & \text{abdeg} & \text{35.3 }\\ \text{abdf} & \text{32.5 } & \text{bcdfg} & \text{35.6 }\\ \text{bf} & \text{27.8} & \text{abcfg} & \text{35.1 }\\ \end{matrix}$$

Perform an analysis of variance on all seven main effects, assuming that interactions are negligible. Use a 0.05 level of significance.

puer Aegyptius, qui sollicitudinem mean senserit, me ad casam proximam duxit. An Egyptian boy, who had sensed my anxiousness, led me to the closest small house. The boy realized why Quintus was anxious and decided to move him away from the crowd. "domine, in hac casa habitat faber, qui Barbillum bene novit. necesse est nobis casam intrare et periculum vitare." Master, in this house lives a smith, who knows Barbillus well. We need to enter the small house and evade the danger.