How did the Emancipation Proclamation and the efforts of African American soldiers affect the course of the war?

How did caudillos come to power in so many new Latin American nations?

Give a geometric argument based on similar triangles to show that the chordal distance between a point z and $\infty$ (that is, the distance between the projection Z and the north pole) is given by $\chi [ z , \infty ] = 2 / \sqrt { 1 + | z | ^ { 2 } }$ [HINT: Draw a cross section of the Riemann sphere and the z-plane containing the north pole, the point z, and its projection Z.]

You're in Manhattan for a job interview. A taxi picks you up from your hotel and takes you x blocks north, then x / 2 blocks east, then x+3 blocks north, then x / 6 blocks east to your destination. Write an expression in terms of x that gives the total number of blocks traveled. Simplify the expression as much as possible. If the total number of blocks you traveled is 19, determine how many blocks you traveled north between the time you entered the cab and the time the cab first turned east.

Explain how American consumer sovereignty operates in the marketplace to determine the success or failure of an entrepreneur.

What was the overall message of the Second Great Awakening, and how did it affect American society?

Use a graphic organizer similar to the one below to identify the effects of the war on the American workforce.

How do large South American cities such as Sao Paulo contribute to increased pollution ?

You are bicycling along a straight north-south road. Let the x-axis point north. Describe your motion in each of the following cases. Example:

$$a_x$$

0 and

$$v_x$$

0 means you are moving north and speeding up. (a)

$$a_x$$

0 and

$$v_x$$

<0. (b)

$$a _ { x } = 0$$

and

$$v_x$$

<0. (c)

$$a_x$$

<0 and

$$v_x$$

=0, (d)

$$a_x$$

<0 and

$$v_x$$

<0. (e) Based on your answers, explain why it is not a good idea to use the expression "negative acceleration" to mean slowing down.

Planet $\mathrm{X}$ rotates in the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs $943.0 \mathrm{~N}$ on the earth weighs $915.0 \mathrm{~N}$ at the north pole of Planet $X$ and only $850.0 \mathrm{~N}$ at its equator. The distance from the north pole to the equator is $18,850$ km, measured along the surface of Planet $X$.
(b) If a $45,000$-$\mathrm{kg}$ satellite is placed in a circular orbit $2000$ km above the surface of Planet $\mathrm{X}$. what will be its orbital period?

Analyzing Why were some Native American groups more nomadic than others?

Starting at the same point in a forest, two hikers take different paths. The first hiker walks due north at a speed of 2 miles per hour. The second hiker walks 60° east of north at a speed of 3 miles per hour. How far apart are the hikers after 1 hour?

What do you think of the peninsulares' role in Latin American society during the 1800s?

How did Latin American society and culture change after World War II?