Determine whether matrix

$$\textbf{A}=\begin{bmatrix}4&2&3\\2&1&2\\-1&2&0\end{bmatrix}$$

is diagonalizable. If it is, determine a matrix $\textbf{P}$ that diagonalizes it and compute $\textbf{P}^{-1}\textbf{AP}$. You can obtain $\textbf{P}^{-1}\textbf{AP}$ directly from careful construction of a diagonal matrix with eigenvalues along the diagonal in the proper order.

What are the largest- and smallest-known values of the mass, luminosity, surface temperature, and diameter of stars (roughly)?

Show that postage of 6 cents or more can be achieved by using only 2-cent and 7-cent stamps.

Simplify the expression.

$$13 ^ { \frac { 1 } { 2 } } \cdot 13 ^ { \frac { 3 } { 2 } }$$

Use a CAS to solve the initial value problem. Plot the solution curves.

$$y^{\prime}=\frac{1}{\sqrt{4-x^{2}}}, \quad y(0)=2$$

Using Newton's Law of Gravitation, if there are two objects exerting the force of gravity on each other and the mass of one of the objects is quadrupled, then the force between them is a. doubled. b. quartered. c. tripled. d. quadrupled.

Find the second derivative of the given function. $f(x)=e^{2 x}+2 e^{-x}$

Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564 m elevation and the village is at 2 096 m. What additional pressure is necessary to deliver this flow? Note: You may assume the free-fall acceleration and the density of air are constant over the given range of elevations.

Give an argument using rules of inference to show that the conclusion follows from the hypotheses. Hypotheses: Everyone in the class has a graphing calculator. Everyone who has a graphing calculator understands the trigonometric functions. Conclusion: Ralphie, who is in the class, understands the trigonometric functions.

A round pencil lying on its side is in neutral equilibrium relative to displacements perpendicular to its length. What is its stability relative to displacements parallel to its length?

Hydrogen chloride, HCl, is a gas at room temperature. Would you expect it to be very soluble or not very soluble in water?

Start by drawing a number line that shows integers from -5 to 5. Then graph each of the following integers on your number line. -4

A drug manufactured by a pharmaceutical company is sold in bulk at a price of $150 per unit. The total production cost (in dollars) for x units in one week is$C ( x ) = 0.02 x ^ { 2 } + 100 x + 3000$ How many units of the drug must be manufactured and sold in a week to maximize the profit? What is the maximum profit?

Consider subsonic Fanno flow accelerated to sonic velocity $(M_a = 1)$ at the duct exit as a result of frictional effects. If the duct length is increased further, will the flow at the duct exit be supersonic, subsonic, or remain sonic? Will the mass flow rate of the fluid increase, decrease, or remain constant as a result of increasing the duct length?