How would you characterize the United States during the Era of Good Feelings?

There is no required size for a United States flag, but the ratio of width to length that is recommended in most cases is 1: 1.9. Write and solve a quadratic equation to find the length and width of a United States flag that has an area of 17.1 square feet.

Assign oxidation states to all of the atoms in the following:

d. $\mathrm{NF}_3$

Assign oxidation states to all of the atoms in the following:

c. $\mathrm{CO}_2$

How would you describe U.S. diplomacy during the Era of Good Feelings?

Assign oxidation states to all of the atoms in the following:

b. $\mathrm{PO}_4{ }^{3-}$

In the upper atmosphere, chlorofluorocarbons such as $\mathrm{CFCl}_3$ absorb sunlight and subsequently fragment, yielding $\mathrm{Cl}$ atoms. The $\mathrm{Cl}$ atoms then destroy ozone by the following mechanism:

$$\begin{aligned} &\mathrm{Cl}(g)+\mathrm{O}_3(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_2(g) \\ &\mathrm{ClO}(\mathrm{g})+\mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{Cl}(g)+\mathrm{O}_2(\mathrm{~g}) \end{aligned}$$

(a) Write the chemical equation for the overall reaction. (b) What is the role of the $\mathrm{G}$ atoms in this reaction? (c) Is $\mathrm{ClO}$ a catalyst or a reaction intermediate? (d) What distinguishes a catalyst from an intermediate?

Show that if an object moves along a straight line in such a way that its velocity is the same at two different times (that is, for a differentiable function v, we are given $v\left(t_{1}\right)=v\left(t_{2}\right)$ for $t_{1} \neq t_{2}$, then there is some intermediate time when the acceleration is zero.

The United States population is approximately $2.99 \times 10^8$. In one year, the United States produced $4.78 \times 10^{11}$ pounds of garbage. Approximately how much garbage did the average American produce that year?

The energy, E, required to compress a gas from a fixed initial pressure $P_0$ to a fixed final pressure $P_F$ through an intermediate pressure $p$ is $^7$

$$E=\left(\frac{p}{P_0}\right)^2+\left(\frac{P_F}{p}\right)^2-1$$

How should $p$ be chosen to minimize the energy?

By what means did the United States and other countries seek to make the world better during the postwar era?

Why must the sum of all the oxidation states of the atoms in a neutral molecule be zero?

Why did the Greek city-states lose power after the Peloponnesian War?

Show that the number of different electron states possible for a given value of $n$ is $2 n^2$.