Use a rotation matrix to rotate the vector

$$\left[\begin{array}{r} 4 \\ -1 \end{array}\right]$$

counterclockwise by the angle $\pi / 3.$

Mayfield Corporation finished job no. 314 on June 1. On June 10, the company sold job no. 314 for $\$ 10,000$, cash. Total manufacturing costs allocated to this job at the time of the sale amounted to $\$ 6,500$.

a. Record the transfer of job no. 314 from Work in Process to Finished Goods on June 1.

Find the rotation–dilation matrix within the given matrix.

$$\left[\begin{array}{rr} 1 & -2 \\ 1 & 3 \end{array}\right]$$

Find the distance between the points.

$$(6.2,5.4),(-3.7,1.8)$$

Refer to the table. Which lap has the slowest time?

Use the data shown in the table that shows the number of bacteria present after a certain number of hours.

Find the equation of the regression line for the data. Then construct a scatter plot of $(x, y)$ and sketch the regression line with it.

Let X={a, b, c}. Define a function S from $\mathcal{P}$(X) to the set of bit strings of length 3 as follows. Let Y$\subseteq$X. If a$\in$Y, set $s_1=0$; If a$\notin$Y, set $s_1=1$; If b$\in$Y, set $s_2=0$; If b$\notin$Y, set $s_2=1$; If c$\in$Y, set $s_3=0$; If c$\in$Y, set $s_3=1$. Define S(Y)=$s_1s_2s_3$.

Prove that S is onto.

Work the given problem on independent events.

According to data from the U.S. Department of Transportation, Delta Airlines was on time approximately 87% of the time in 2012 . Use this information, and assume that the event that a given flight takes place on time is independent of the event that another flight is on time to answer the following questions

(a) Elisabeta Gueyara plans to visit her company's branch offices; her journey requires 3 separate flights on Delta Airlines. What is the probability that all of these flights will be on time?

(b) How reasonable do you believe it is to suppose the independence of being on time from flight to flight?

The distance from the surface of a lens to the focal point is the

Make sense of problems. A sale on dog food that costs $10 a bag says buy 1, get one$$$\frac { 1 } { 2 }$ off. What is the true percent discount on the dog food?

Find the rotation–dilation matrix within the given matrix.

$$\left[\begin{array}{rr} 1 & 3 \\ -3 & 1 \end{array}\right]$$

Find the distance between the two points. If necessary, you may draw graphs but you shouldn't need to use the distance formula.

$(0,0)$ and $(3,4)$

The numbers in Set N are multiples of 5.

The numbers in Set P are multiples of 9.

Which number of the three possibilities could be a number of both Set N and Set P ?

A. 27

B. 25

C. 90

Solve the problem.

The polar equation

$$r=\frac{a\left(1-e^2\right)}{1+e \cos \theta}$$

can be used to graph the orbits of the planets, where $a$ is the average distance in astronomical units from the sun and $e$ is a constant called the eccentricity. The sun will be located at the pole.

Plot the orbits of Earth, Jupiter, Uranus, and Pluto on the same polar grid. How does Earth's distance from the sun compare to the other planets' distances from the sun?