Explain why a spinning top will not remain in motion forever.

What are the three functional parts of the cerebellum, and what are the functions of each?

Choose the correct verb from the pair shown in parentheses.

Sometimes a calf will (rise, raise) from the water on its mother's back.

For nuclei with a mass number greater than 40, which of the following statements is correct: (a) the number of protons is approximately equal to the number of neutrons; (b) the number of protons exceeds the number of neutrons; (c) all such nuclei must be stable up to Z = 92; or (d) none of the preceding?

Evaluate the function at each specified value of the independent variable and simplify.

$$g(y)=7-3 y$$

$(c)$ $g(s+2)$

A certain crystal has a set of planes spaced $0.30 \mathrm{~nm}$ apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction pattern occurs at $\varphi=42^{\circ}$. What are the de Broglie wavelength and kinetic energy of the neutrons?

Suppose a ball attached to a spring is pulled down 5 inches and released and the resulting simple harmonic motion has a period of ten seconds. Write an equation of the ball's simple harmonic motion.

Draw the products you would expect from conrotatory and disrotatory cyclizations of (2Z,4Z,6Z)-2,4,6-octatriene. Which of the two paths would you expect the thermal reaction to follow?

Starting at the same time and place, Abe and Bob race, running at velocities $u(t)=4 /(t+1) \mathrm{mi} / \mathrm{hr}$ and $v(t)=4 e^{-t / 2} \mathrm{mi} / \mathrm{hr}$, respectively, for $t \geq 0$. (a). Who is ahead after $t=5 \mathrm{hr}$ ? After $t=10 \mathrm{hr}$ ? (b). Find and graph the position functions of both runners. Which runner can run only a finite distance in an unlimited amount of time?

Harmonic Motion The motion of an oscillating weight suspended by a spring was measured by a motion detector. The data collected and the approximate maximum (positive and negative) displacements from equilibrium are shown in the figure. The displacement $y$ is measured in feet and the time $t$ is measured in seconds.

Use a graphing utility to graph the model in part (c). Compare the result with the data in the figure.

Is each of these statements true? If not, explain why.
(d) A temperature rise of $10^{\circ} \mathrm{C}$ doubles the rate of any reaction.

List the elements in each of the sets. The set of outcomes of tossing three (a) distinguishable coins (b) indistinguishable coins.

In the following exercise, evaluate (if possible) the function at the given value(s) of the independent variable. Simplify the results.

$$f(x)=\sqrt{x+3}$$

$$f(-2)$$

For the matrix A and vector $x_0$, compute the first four iterations of the Power Method, and then explain the behavior that you observe.

$$A=\left[\begin{array}{rr} 1 & 1 \\ 0 & -1 \end{array}\right], \ \mathbf{x}_{0}=\left[\begin{array}{l} 0 \\ 1 \end{array}\right]$$