Determine whether the following statements are true and give an explanation or counterexample.

$| \mathbf { u } \times \mathbf { v } |$ is less than both $|u|$ and $|v|$.

Write the numeral as a Roman numeral.

A particle is in the first excited ( $n=2)$ state of a onedimensional box that has length $L$. (The box has one end at the origin and the other end on the positive $x$ axis.) . Find \left\langle x^2\right\rangle$.

Determine whether the statement is true and give an explanation or counterexample. If $u \neq 0$ and $u+v=0$, then $u$ and $v$ are parallel.

Write the symbol for the element: iron

Use trigonometric identities to find the below indicated value(s). $\newline$ If $\cos \theta=\frac{7}{25}$ and the terminal side of $\theta$ lies in QIV, find $\cot \theta$.

Identify each horizontal and vertical translation of the parent function y=|x|. y=|x-2|+5

A sky diver falls through the air. As the speed of the sky diver increases, what happens to the sky diver’s acceleration? What is the acceleration when the sky diver reaches terminal speed?

Two 10 copper wires (2.588 mm in diameter) are placed parallel in the air with a separation distance "d" between them. If the inductance of each wire is $1.2 \mu \mathrm{H} / \mathrm{m}$, compute

(a) $L_{\text {in }}$ and $L_{\text {ext }}$ per meter for each wire

(b) The separation distance $d$

Some people with a deficit of IgA exhibit recurrent paranasal sinus and respiratory tract infections. Explain these symptoms.

The terminal side of $\theta$ in standard position contains the given point. Find the values of the six trigonometric functions of $\theta .$ $( \sqrt { 3 } , - 1 )$

What is the pulse deficit if an apical pulse is 112 and the radial pulse is 88?

Write the symbol for the element: tin

A wall has inner and outer surface temperatures of 16 and $6^{\circ} \mathrm{C}$, respectively. The interior and exterior air temperatures are 20 and $5^{\circ} \mathrm{C}$, respectively. The inner and outer convection heat transfer coefficients are 5 and $20 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, respectively. Calculate the heat flux from the interior air to the wall, from the wall to the exterior air, and from the wall to the interior air. Is the wall under steady-state conditions?