(a) Calculate the electric field strength near a 10.0 cm diameter conducting sphere that has 1.00 C of excess charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

The practical limit to an electric field in air is about $3.00 \times 10 ^ { 6 } \mathrm { N } / \mathrm { C }$. Above this strength, sparking takes place because air begins to ionize. (a) At this electric field strength, how far would a proton travel before hitting the speed of light (ignore relativistic effects)? (b) Is it practical to leave air in particle accelerators?

Two sides of a parallelogram coincide with the position vectors for u and v. Find the area of the parallelogram.

$$\mathbf{u}=\left[\begin{array}{l} 4 \\ -1\\ 2 \end{array}\right], \ \mathbf{v}=\left[\begin{array}{l} 0 \\ 1 \\ 2 \end{array}\right]$$

Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be $1.67 \times 10^{-27} \mathrm{kg}.$

Salicylic acid, $\mathrm{HOC}_{6} \mathrm{H}_{4} \mathrm{CO}_{2} \mathrm{H}$, and its derivatives have been used as pain relievers for a long time. Salicylic acid occurs in small amounts in the leaves, bark, and roots of some vegetation (most notably historically in the bark of the willow tree). Extracts of these plants have been used as medications for centuries. The acid was first isolated in the laboratory in 1838. (a) Both functional groups of salicylic acid ionize in water, with $K_{\mathrm{a}}=1.0 \times 10^{-3}$ for the$-\mathrm{CO}_{2} \mathrm{H}$ group and 4.2 $\times 10^{-13}$ for the −OH group. What is the pH of a saturated solution of the acid (solubility = 1.8 g/L). (b) Aspirin was discovered as a result of efforts to produce a derivative of salicylic acid that would not be irritating to the stomach lining. Aspirin is acetylsalicylic acid, $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{CO}_{2} \mathrm{H}$. The −$\mathrm{CO}_{2} \mathrm{H}$ functional group is still present, but its acidity is reduced, $K_{\mathrm{a}}=3.0 \times 10^{-4}$. What is the pH of a solution of aspirin with the same concentration as a saturated solution of salicylic acid (See Part a). (c) Under some conditions, aspirin reacts with water and forms a solution of salicylic acid and acetic acid: $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{CO}_{2} \mathrm{H}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$ $\mathrm{HOC}_{6} \mathrm{H}_{4} \mathrm{CO}_{2} \mathrm{H}(a q)+\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(a q)$ i. Which of the acids, salicylic acid or acetic acid, produces more hydronium ions in such a solution? ii. What are the concentrations of molecules and ions in a solution produced by the hydrolysis of 0.50 g of aspirin dissolved in enough water to give 75 mL of solution?

More than one choice may apply. Which of the following cell types are granulocytes? a. Lymphocytes b. Platelets c. Eosinophils d. Basophils

Find $B = (b_1, b_2)$ such that $\mathbf{v}=\overrightarrow{A B}$.

$$\mathbf{v}=\left[\begin{array}{c} 2 \\ 5 \end{array}\right]$$

and $A=(1,-2)$.

For what values of $\lambda$ is the matrix

$$A=\left[\begin{array}{cc} \lambda-4 & -1 \\ 2 & \lambda-1 \end{array}\right]$$

singular? Find $A^{−1}$ if A is nonsingular.

Dolphins make sounds in air and water. What is the ratio of the wavelength of a sound in air to its wavelength in seawater? Assume air temperature is $20.0^{\circ} \mathrm{C}.$

For the following exercise, use the Equation to find the slope of the secant line between the values $x_{1}$ and $x_{2}$ for the function y = f(x). $f(x)=6 x^{2 / 3}+2 x^{1 / 3} ; x_{1}=1, x_{2}=27$

Calculate the magnitude of the electric field 2.00 m from a point charge of 5.00 mC (such as found on the terminal of a Van de Graaff).

Many plastic materials are organic polymers that contain carbon and hydrogen. The oxidation of these plastics in air to form carbon dioxide and water is a spontaneous process; however, plastic materials tend to persist in the environment. Explain.

(a) What is the average metabolic rate in watts of a man who metabolizes 10,500 kJ of food energy in one day? (b) What is the maximum amount of work in joules he can do without breaking down fat, assuming a maximum efficiency of 20.0%? (c) Compare his work output with the daily output of a 187-W (0.250-horsepower) motor.

At what distance is the electrostatic force between two protons equal to the weight of one proton?