Exam 12: Vectors and Matrices

In the figure below, each square is 1 units along each side. In component form, .

A retailer's total monthly sales of three different models of television is given by the vector . If the sales for each model go down by 5% the next month, what is , the next month's total sales? Round entries to the nearest whole number.

A snow cone stand sells three sizes of snow cones: small, medium, and large. Let give the number of each type of cone sold in one day. Let give the price (in dollars) charged for each size of snow cone, give the cost (also in dollars) of making each size of snow cone, and give the maximum number of each size that can be sold (because of the number of each size cup on hand). How much money was spent making the small snow cones that day?

Let and . Find such that .

For and , .

A snow cone stand sells three sizes of snow cones: small, medium, and large. Let give the number of each type of cone sold in one day. Let give the price charged for each size of snow cone, give the cost of making each size of snow cone, andGive the maximum number of each size that can be sold (because of the number of each size cup on hand.) Let . Which of the following gives the maximum amount of money that can be received from one day's sales?

A particle in equilibrium is acted upon by three forces, two of which have components and . The components of the third must be .

If and , find

If and , then what is ?

A country has two main political parties. The vector gives the number of people who are members of the first party, the second party, and neither party, respectively. Suppose . What percent of the members of the first party switch to the second party each year?

Find the length of the vector if and .

Jack and Jill begin walking away from a water well. Jill walks 3 meters north, and then 12 meters east. When Jill stops, Jack is twice as far from the well as she is. How far is Jack from the well?

For and , what is ?

A man is sitting 6 meters above the ground in a tree which is 10 meters directly south of the fence corner of a field. A bird is spotted 4 meters above the ground and 4 meters directly north of the fence corner. In what direction must the man face to look directly at the bird? Round your answer to 3 decimal places.

There are six people taking a vocational exam with both oral and written parts. Their scores (out of 100) on the written section are given by the vector . Their scores (out of 100) on the oral section are given by the vector . Find the vector giving their composite score if the written part counts twice as much as the oral part.

Given , , and what is ?

Let Give the profit a salesman makes from selling three different models of computers. Let give the number of each computer model sold each month. What does represent?

Simplify

Let and . Write the displacement vector in component form.

The rectangle with vertices (1,0), (1,4), (2,0), and (2,4) is rotated through an angle of about the origin. What are the coordinates of the new rectangle?