What caused the spread of Christianity through the Roman empire?

Consider three successive coordinate rotations using the same angle a. Show that the product $\mathbf { R } \mathbf { R } \mathbf { R }$ of the rotation matrix $\mathbf { R } ( a )$ equals $\mathbf { R } ( 3 a ) .$

Why is a second bee sting more dangerous than the first for a person who is allergic to bee sting?

As a fuel, H2(g) produces only nonpolluting H2O(g) when it burns. Moreover, it combines with O2(g) in a fuel cell to provide electrical energy. Calculate $\Delta \mathrm { H } ^ { \circ } , \Delta \mathrm { S } ^ { \circ } ,$ and $\Delta \mathrm { G } ^ { \circ }$ per mole of H2 at 298 K.

The amount of money Hoshi's Music Hall took in from 2003 to 2010 can be modeled by

$$M ( x ) = - 2.03 x ^ { 3 } + 50.1 x ^ { 2 } - 214 x + 4020$$

where x is the years since 2003. Graph the function using your calculator.

Suppose a particle called a kaon is created by cosmic radiation striking the atmosphere. It moves by you at 0.980 c, and it lives $1.24\times 10^{-

8}$ when at rest relative to an observer. How long does it live as you observe it?

Prove that the two triangular halves of the truss are congruent.

Convert the given measure. 4.58 m=_______ cm

Simplify. Assume that variable exponents represent positive integers.

$$y ^ { 3 } \cdot y ^ { 2 }$$

Select the best answer. A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize? (a) 0.25 (b) 1.00 (c)

$$\left( \begin{array} { l } { 4 } \\ { 1 } \end{array} \right) ( 0.25 ) ^ { 1 } ( 0.75 ) ^ { 3 }$$

(d)

$$\left( \begin{array} { l } { 4 } \\ { 1 } \end{array} \right) ( 0.25 ) ^ { 3 } ( 0.75 ) ^ { 1 }$$

(e)

$$( 0.75 ) ^ { 3 } ( 0.25 ) ^ { 1 }$$

Find the possible values for a if the points with the given coordinates are the indicated distance apart. (a, -6), (-5, 2); d = 10

Solve the inequality.

$$x^2 – 12x + 27 < 0$$

The city council of a large city needs to know whether its residents will support the building of three new schools. The council decides to conduct a survey of a sample of the city's residents. Which procedure would be most appropriate for obtaining a sample of the city 's residents ? a. Survey a random sample of teachers who live in the city. b. Survey 100 individuals who are randomly selected from a list of all people living in the state in which the city in question is located. c. Survey a random sample of perso ns within each neighborhood of the city. d. Survey every tenth person who enters City Hall on a randomly selected day.

A box contains 8 red chips, 6 blue chips, and 12 white chips. Three chips are randomly drawn from the box and are not replaced. P(blue, blue)