(a) Quasars are some of the most distant objects in the Universe. In which direction do the light waves from quasars most likely shift? (b) A scientist observing a quasar in 2009 is actually seeing the quasar as it existed in the early Universe. Explain why this is so.

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. $y=-\sqrt{16-x^{2}} ; y=0 ; 0 \leq x \leq 4$

A new object is discovered in the Solar System and needs to be classified as a comet, an asteroid, a planet, or a dwarf planet. What information about the object would you want to collect to properly classify it?

Write and solve the Euler equations to make the following integrals stationary. In solving the Euler equations, the integrals. $\int_{x_{1}}^{x_{2}} \sqrt{x} \sqrt{1+y^{\prime 2}} d x$

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection. Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form. $y^{\prime \prime}+2 y^{\prime}+10 y=100 \cos 4 x$

Show that if the line through the origin and the point z is rotated $90^{\circ}$ about the origin, it becomes the line through the origin and the point iz. This fact is sometimes expressed by saying that multiplying a complex number by i rotates it through $90^{\circ}$. Use this idea in the following problem. Let $z=a e^{i \omega t}$ be the displacement of a particle from the origin at time t. Show that the particle travels in a circle of radius a at velocity $v=a \omega$ and with acceleration of magnitude $v^{2} / a$ directed toward the center of the circle.

Show that each of the following matrices is orthogonal and find the rotation and/or reflection it produces as an operator acting on vectors. If a rotation, find the axis and angle; if a reflection, find the reflecting plane and the rotation, if any, about the normal to that plane.

$$\frac{1}{9}\left(\begin{array}{rrr} -1 & 8 & 4 \\ -4 & -4 & 7 \\ -8 & 1 & -4 \end{array}\right)$$

Find $\lim _{x \rightarrow 0} \frac{x^{2} e^{x}}{\cos x-1}$. (A) $-\infty$ (B) -2 (C) 0 (D) 1

Many companies acquire software to help them monitor and control their costs and as an aid to their accounting systems. One company that supplies such software is proDacapo (prodacapo.com). There are many other such vendors. Access proDacapo’s website, click on “Products,” then click on “Prodacapo Process Management,” and review the information displayed. How is process management software helpful to businesses? Explain with reference to costs, efficiency, and examples, if possible.

Find the following gradients in two ways and show that your answers are equivalent. $\nabla x$

You are playing the fortune-teller at your school's winter carnival. Some of your friends want to find out what is going to happen to them in the future. Write at least three predictions for each of the people listed below. The first one has been started for you. Nombre de dos amigos(as): _____ y _____ Predicciones: _____

Why must a company use predetermined overhead rates when using job order costing?

Find the real and imaginary parts u(x, y) and v(x, y) of the following functions. $\cosh z$

As the driver steps on the gas pedal, a car of mass 1160 kg accelerates from rest. During the first few seconds of motion, the car's acceleration increases with time according to the expression

$$a=1.16 t-0.210 t^{2}+0.240 t^{3}$$

where t is in seconds and a is in $\mathrm{m} / \mathrm{s}^{2}.$ (a) What is the change in kinetic energy of the car during the interval from t = 0 to t = 2.50 s? (b) What is the minimum average power output of the engine over this time interval? (c) Why is the value in part (b) described as the minimum value?