Balance the following oxidation-reduction equations. The reactions occur in acidic solution. a. $\mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}+\mathrm{C}_2 \mathrm{O}_4{ }^{2-} \longrightarrow \mathrm{Cr}^{3+}+\mathrm{CO}_2$ b. $\mathrm{Cu}+\mathrm{NO}_3{ }^{-} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{NO}$ c. $\mathrm{MnO}_2+\mathrm{HNO}_2 \longrightarrow \mathrm{Mn}^{2+}+\mathrm{NO}_3$ d. $\mathrm{PbO}_2+\mathrm{Mn}^{2+}+\mathrm{SO}_4{ }^{2-} \longrightarrow \mathrm{PbSO}_4+\mathrm{MnO}_4{ }^{-}$ e. $\mathrm{HNO}_2+\mathrm{Cr}_2 \mathrm{O}_7{ }^{2-} \longrightarrow \mathrm{Cr}^{3+}+\mathrm{NO}_3^{-}$

Plot the point in polar coordinates and find the corresponding rectangular coordinates for the point.

(4,3$\pi$/6)

Why are the triple point temperature and the normal freezing point very close in temperature for most substances?

For complexes of the same metal ion with no change in oxidation number, the stability increases as the number of electrons in the $t_2 g$ orbitals increases. Which complex in each of the following pairs of complexes is more stable? (a) $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ or $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$ (b) $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ or $\left[\mathrm{CoF}_6\right]^{3-}$ (c) $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{4-}$ or $\left[\mathrm{MnCl}_6\right]^{4-}$

What regulatory body did Dodd-Frank create?

Ball B, moving in the positive direction of an x axis at speed v, collides with stationary ball A at the origin. A and B have different masses. After the collision, B moves in the negative direction of the y axis at speed v/2. Show that the speed of A cannot be determined from the given information.

The oxidation state of cobalt in each of the following species is $+3$. Determine the overall charge on each complex:

$\left.\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^?,\left[\mathrm{Co}(\mathrm{CN})_6\right]^?,\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Br}\right]_3\right]^?,\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]^?,\left[\mathrm{Co}(\mathrm{en})_3\right]^?,\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^?,\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}\right]^{\text {? }}$.

If a sample of radioactive material has a half-life of one week, how much of the original sample will be left at the end of the second week? The third week? The fourth week?

Suppose that a surface has an equation in cylindrical coordinates of the form z = f (r). Explain why it must be a surface of revolution.

A student holds one end of a 4.5-m rope with a mass of $1.0 \mathrm{~kg}$. The other end is connected to one side of a spring scale, which is attached to a wall. The scale reads $15.0 \mathrm{~N}$. The student moves her hand up, down, and back to equilibrium all within $1.0$ second, generating a wave that moves down the rope. Determine the speed, frequency, and wavelength of the wave.

We provide a sample mean, sample size, population standard deviation, and confidence level. In each case, use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. $\bar{x}=55$, $n=16$, $\sigma=5$, confidence level = 99%

Find the volume of the solid inside the surface r²+z²=4 and outside the surface r=2 cos θ.

Use oxidation numbers to balance the following equations:

a. $\text{KClO}_{3}(\text{aq})+\text{HBR(aq)}\rightarrow\text{Br}_{2}(\text{l})+\text{KCl}(\text{aq})+\text{H}_{2}\text{O}(\text{l})$

b. $\text{Cu(s)}+\text{HNO}_{3}(\text{aq})\rightarrow\text{Cu(NO}_{3})_{2}(\text{aq})+\text{NO}_{2}(\text{g})+\text{H}_{2}\text{O}(\text{l})$

c. $\text{C}_{2}\text{H}_{6}(\text{g})+\text{O}_{2}(\text{g})\rightarrow\text{CO}_{2}(\text{g})+\text{H}_{2}\text{O}(\text{g})$

For each of the following oxidation-reduction reactions of metals with nonmetals, identify which element is oxidized and which is reduced. a. $6 \mathrm{Na}(\mathrm{s})+\mathrm{N}_2(\mathrm{~g}) \rightarrow 2 \mathrm{Na}_3 \mathrm{~N}(\mathrm{~s})$ b. $\mathrm{Mg}(s)+\mathrm{Cl}_2(g) \rightarrow \mathrm{MgCl}_2(s)$ c. $2 \mathrm{Al}(s)+3 \mathrm{Br}_2(\mathrm{l}) \rightarrow 2 \mathrm{AlBr}_3(s)$ d. $4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{Fe}_2 \mathrm{O}_3(s)$