Perform the indicated addition or subtraction. (-8 + 4i) - (7 - i)

In lines 9-15 of "The Seven Ages of Mat do the speaker's words reveal about his attitude coward lovers and soldiers?

(a) If you were stranded on an island with a pair of 3.5 D reading glasses, could you make a useful telescope? If so, what would be the length of the telescope and what would be the angular magnification? (b) Answer the same questions if you also bad a pair of 1.3 D reading glasses.

The price of a certain brand of printers is normally distributed with mean cost of $215 and standard deviation$35. What proportion of printers cost more than $250?

Show that $\iint_{S} z^{2} \mathrm{d} S=\frac{2}{3} \pi$, where S is the surface of the sphere $x^{2}+y^{2}+z^{2}=1, z \geqslant 0$.

A model car has a windshield with dimensions

$$\frac { 1 } { 18 }$$

the size of a real car windshield. The rectangular windshield of the real car has an area of about 2,318 square inches, with a width of 61 inches. What are the side lengths of the model car's windshield? Round to the nearest hundredth. Justify your answer.

Use a parametrization to find the flux

$$\iint _ { S } \mathbf { F } \cdot \mathbf { n } d \sigma$$

across the surface in the specified direction.

$$\mathbf { F } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$$

outward through the portion of the cylinder

$$x ^ { 2 } + y ^ { 2 } = 1$$

cut by the planes z = 0 and z = a.

The mass of a sample of aluminum is 12.15 g and its volume is 4.5 cm$^3$. What is the density of aluminum?

(a) Show that all three $C_{2}$ operations in the group $D_{2h}$ belong to the same class. (b) Show that all three $\sigma{\tau}$ operations in the group $D_{2h}$ belong to the same class.

An individual heterozygous for four genes

$$A / a \cdot B / b C / c \cdot D / d$$

is testcrossed with

$$a / a \cdot b / b \cdot c / c \cdot d / d$$

and 1000 progeny are classified by the gametic contribution of the heterozygous parent as follows:

$$\begin{array} { l l } { a \cdot B \cdot C \cdot D } & { 42 } \\ { A \cdot b \cdot c \cdot d } & { 43 } \\ { A \cdot B \cdot C \cdot d } & { 140 } \\ { a \cdot b \cdot c \cdot D } & { 145 } \\ { a \cdot B \cdot c \cdot D } & { 6 } \\ { A \cdot b \cdot C \cdot d } & { 9 } \\ { A \cdot B \cdot c \cdot d } & { 305 } \\ { a \cdot b \cdot C \cdot D } & { 310 } \end{array}$$

a. Which genes are linked? b. If two pure-breeding lines had been crossed to produce the heterozygous individual, what would their genotypes have been? c. Draw a linkage map of the linked genes, showing the order and the distances in map units. d. Calculate an interference value, if appropriate.

Nitric acid hydrates have received much attention as possible catalysts for heterogeneous reactions that bring about the Antarctic ozone hole. Worsnop et al. (Science 259,71(1993)) investigated the thermodynamic stability of these hydrates under conditions typical of the polar winter stratosphere They report thermodynamic data for the sublimation of mono-, di-, and trihydrates to nitric acid and water vapours, $\mathrm{HNO}_3 n \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightarrow \mathrm{HNO}_{3}(\mathrm{g})+n \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ for n = 1, 2, and 3. Given $\Delta_1 G^{\circ}$ and $\Delta_1 H^{\circ}$ for these reactions at 220 K use the Gibbs-Helmholtz equation to compute $\Delta_1 G^{\circ}$ for each at 190 K.

$$\begin{array}{ccc}{n} & {1} & {2} & {3} \\ {\Delta_1 G^{\circ}/(kJ m o l^{-1} )} & {46.2} & {69.4} & {93.2} \\ {\Delta_1 H^{\circ}/(kJ m o l^{-1} )} &{127} & {188} & {237}\end{array}$$

What color name can be unscrambled with the letters? (g o n r e)

Fill in the blank with the term that best completes the following sentence. _________ is a measure of the gravitational force on an object.

The product, P(n) , of two numbers is represented by the expression 2n^2-4n+3 , where n is a real number.

a) If one of the numbers is represented by n-3 , what expression represents the other number?

b) What are the two numbers if n=1?