At $500^{\circ} \mathrm{C}$, the reaction

$$\mathrm{SO}_2(g)+\mathrm{NO}_2(g) \rightleftharpoons \mathrm{NO}(g)+\mathrm{SO}_3(g)$$

has $K_{\mathrm{oq}}=81$. What will be the equilibrium concentrations of the four gases if the two reactants begin with equal concentrations of $0.50~M$ ?

Scores on a test are normally distributed with a mean of 70 and a standard deviation of 10 . Determine the probability of the given event.

A randomly selected student scored between 70 and 90.

Two identical tetrahedral dice are rolled. Their four vertices are clearly labelled 1, 2, 3, and 4. The result when one die comes to rest is the number on the uppermost vertex. Let X be the sum of the scores on the two dice. What are the possible values of X?

General expressions for the components of a light ray's velocity as measured in reference frame S are

$$\begin{aligned} & v_x=c \sin \theta \cos \phi \\ & v_y=c \sin \theta \sin \phi \\ & v_z=c \cos \theta \end{aligned}$$

where $\theta$ and $\phi$ are the angular coordinates in a spherical coordinate system.

(a) Prove that

$$v=\sqrt{v_x^2+v_y^2+v_z^2}=c .$$

(b) Using the velocity transformation equations prove that, as measured in reference frame $S^{\prime}$,

$$v^{\prime}=\sqrt{v_x^{\prime 2}+v_y^{\prime 2}+v_z^{\prime 2}}=c,$$

and so confirm that the speed of light has the constant value c in all frames of reference.

Find the distinct singular values of A.

$$A=\left[\begin{array}{ll}{3} & {0} \\ {0} & {4}\end{array}\right]$$

.

Work with a partner. Say whether it is cold or hot, according to the temperature given.

modelo: $32^{\circ} \mathrm{F} / 0^{\circ} \mathrm{C}$

$\hspace{32pt}$ Hace frío.

$$88^{\circ} \mathrm{F} / 32^{\circ} \mathrm{C}$$

The Lunar Roving Vehicle used in NASA's late Apollo missions reached an unofficial lunar land speed of 5.0 m/s by astronaut Eugene Cernan. If the rover was moving at this speed on a flat lunar surface and hit a small bump that projected it off the surface at an angle of 20°, how long would it be "airborne" on the Moon?

Consider the following equation:

$$\mathrm{C}_3 \mathrm{H}_8(g)+5 \mathrm{O}_2(g) \rightarrow 3 \mathrm{CO}_2(\mathrm{~g})+4 \mathrm{H}_2 \mathrm{O}(g)$$

(a) How many liters of oxygen are required to react with $7.2 \mathrm{~L} \mathrm{~C}_3 \mathrm{H}_8$ ? Both gases are at STP.
(b) How many grams of $\mathrm{CO}_2$ will be produced from $35 \mathrm{~L} \mathrm{~C}_3 \mathrm{H}_8$ if both gases are at STP?
(c) How many liters of water vapor can be produced when $15 \mathrm{~L} \mathrm{~C}_3\mathrm{H}_8$ are reacted with $15 \mathrm{~L} \mathrm{O}_2$ ? All gases are at the same temperature and pressure.

What is a recursive equation for the sequence $4,-6.6,10.89,-17.9685, \ldots$?

(A) $a_n=(-2.6) a_{n-1}$

(B) $a_n=(-1.65) a_{n-1}$

(C) $a_n=(2.6) a_{n-1}$

(D) $a_n=(1.65) a_{n-1}$

Rewrite the following sentence, altering the position of the italicized adjectives. Be sure that the adjectives modify the same noun in your sentence as in the original. Make any necessary changes in wording and punctuation.

The bird, cold and hungry, pecked the ground for worms.

Find the midpoint of each pair of points.

$(-4,4,3),(5,-1,3)$

Find the LCM of each pair by listing multiples. 10, 36

Write the initiation, propagation, and termination steps involved in the monobromination of 2,3dimethylbutane to give 2-Bromo-2,3-dimethyl butane.

In which situation might dispersion be a problem in focusing a camera lens: (a) taking a color photograph, or (b) taking a black and white photograph? Explain your answer.