If a compressive force of $3.3 \times 10^4 \mathrm{~N}$ is exerted on the end of a $22 \mathrm{~cm}$ long bone of cross-sectional area $3.6 \mathrm{~cm}^2$, $(a)$ will the bone break, and $(b)$ if not, by how much does it shorten?

For the point given in polar coordinates, state the axis on which the point lies if it is graphed in a rectangular coordinate system. Also state whether it is on the positive portion or the negative portion of the axis. $\left(8,450^{\circ}\right)$

Find an equation of the tangent line to the graph of the function at the given point.

$$\begin{matrix} \text{Function} & \text{Point}\\ \text{y=tan x} & \text{}{\left(-\frac{\pi}{4},-1\right)}\\ \end{matrix}$$

Determine a rotation $\mathbf{x}=P \mathbf{x}^{\prime}$ that removes the cross-product terms, and give its equation in the $x^{\prime} y^{\prime} z^{\prime}$-system. Name the quadric.

$$2 x^2+3 y^2+23 z^2+72 x z+150=0$$

When did the French get involved in the American Revolution?

Solve the first-order differential equation by separating variables.

$$y'=\dfrac{x^2+1}{3y^2}$$

Complete each sentence by writing the form of the verb indicated in parentheses.

The art students are _________ pictures of buildings. (present participle of sketch)

Perform the given translation on (3, 1). Give the coordinates of the translated point. 2 units right.

Write two different proportions using each set of numbers. Use cross products to justify your answer. A. $1.80,$1.20, 14, 21 B. 1, 3.5, 31.50, 9.0 C. 11.7, 8424, 0.02, 14.4

When writing electron confi gurations for elements in period 4, why are electrons placed in the 4s sublevel before the 3d sublevel?

Complete each sentence by writing the form of the verb indicated in parentheses.

_________ anyone _________ my little brother? (present perfect of see)

A. Millikan, although best known for his "oil-drop experiment," which measured the charge of an electron, also performed pioneering research on the photoelectric effect. In experiments on lithium, for example, Millikan observed a maximum kinetic energy of $0.550 \mathrm{~eV}$ when electrons were ejected with $433.9-\mathrm{nm}$ light. When light of $253.5 \mathrm{~nm}$ was used, he observed a maximum kinetic energy of $2.57 \mathrm{~eV}$. (a) What is the work function, $W_{0}$, for lithium, as determined from Millikan's results? (b) What maximum kinetic energy do you expect Millikan found when he used light with a wavelength of $365.0 \mathrm{~nm}$ ?

In given exercise, the matrix product AX performs the translation of the point (x, y) to the point (x+h, y+k), when

$$A=\left[\begin{array}{lll}1 & 0 & h \\0 & 1 & k \\0 & 0 & 1\end{array}\right] \text { and } X=\left[\begin{array}{l}x \\y \\1\end{array}\right] \text {. }$$

Predict the coordinates of the translated point.

$$A=\left[\begin{array}{rrr}1 & 0 & -3 \\ 0 & 1 & 4 \\ 0 & 0 & 1\end{array}\right], \quad X=\left[\begin{array}{r}2 \\ -4 \\ 1\end{array}\right]$$

Find an equation of the tangent line to the graph at the given point.

Rotated ellipse: $7x^2-6\sqrt{3}xy+13y^2-16=0$ Point: $\left(\sqrt{3},1\right)$