The rocket is traveling around the earth in free flight along the elliptical orbit. If the rocket has the orbit shown, determine the speed of the rocket when it is at A and at B.

The rocket shown is originally in a circular orbit $6 \mathrm{Mm}$ above the surface of the earth. It is required that it travel in another circular orbit having an altitude of $14 \mathrm{Mm}$. To do this, the rocket is given a short pulse of power at $A$ so that it travels in free flight along the dashed elliptical path from the first orbit to the second orbit. Determine the necessary speed it must have at $A$ just after the power pulse, and the time required to get to the outer orbit along the path $A A^{\prime}$. What adjustment in speed must be made at $A^{\prime}$ to maintain the second circular orbit?

The rocket shown is originally in a circular orbit $6 \mathrm{Mm}$ above the surface of the earth. It is required that it travel in another circular orbit having an altitude of $14 \mathrm{Mm}$. To do this, the rocket is given a short pulse of power at $A$ so that it travels in free flight along the gray elliptical path from the first orbit to the second orbit. Determine the necessary speed it must have at $A$ just after the power pulse, and the time required to get to the outer orbit along the path $A A^{\prime}$. What adjustment in speed must be made at $A^{\prime}$ to maintain the second circular orbit?

Graph $y=x^{2}$ in the graphing window $-10 \leq x \leq 10$, $-10 \leq y \leq 10$, without drawing the x- and y-axes. Adjust the graphing window for $y=2(x-1)^{2}+3$ so that (without the axes showing) the graph looks identical to that of $y=x^{2}$.

Draw all possible skeletons for a 6-C compound with

A 5-C chain and 2 double bonds,

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If a Markov chain is regular, then it is absorbing.

A certain fluid has a density of 1 080 kg/m$^3$ and is observed to rise to a height of 2.1 cm in a 1.0-mmdiameter tube. The contact angle between the wall and the fluid is zero. Calculate the surface tension of the fluid.

Identify the conic section that the equation represents.

$$\frac { ( x + 2 ) ^ { 2 } } { 6 ^ { 2 } } + \frac { ( y - 7 ) ^ { 2 } } { 8 ^ { 2 } } = 1$$

Prove that the following groups are not cyclic: (a) Z_2 × Z_2; (b) Z_2 × Z; (c) Z × Z; (d) Φ(2^n) for n ≥ 3.

Write a letter to a friend describing your recent visit to Japan. Be sure to include details you learned.

Prove that if the block is released from rest at point $B$ of a smooth path of arbitrary shape, the speed it attains when it reaches point $A$ is equal to the speed it attains when it falls freely through a distance $h ;$ i.e., $v=\sqrt{2 g h}$. Where $h$ is the vertical distance of point $B$ from point $A$.

The smooth surface of the vertical cam is defined in part by the curve $r=(0.2 \cos \theta+0.3) \mathrm{m}$. If the forked rod is rotating with a constant angular velocity of $\dot{\theta}=4 \mathrm{rad} / \mathrm{s}$, determine the force the cam and the rod exert on the $2-\mathrm{kg}$ roller when $\theta=30^{\circ}$. The attached spring has a stiffnesss $k=30 \mathrm{~N} / \mathrm{m}$ and an unstretched length of $0.1 \mathrm{~m}$.

State the law of universal gravitation, and use examples to explain how changes in mass and changes in distance affect gravitational force.

With your teacher's help, use a microphone and an oscilloscope or a CBL interface to obtain an image of a sound. Determine the frequency and wavelength of the sound.