Exam 12: Vectors and Matrices

A particle is acted on by two forces, one of them to the west and of magnitude 0.5 dynes (a dyne is a unit of force), and the other in the direction 60 north of east and of magnitude 1 dyne. A third force acting upon the particle that would keep it at equilibrium has a magnitude of ______ dynes and points _____ (north / south / east / west). Round the first answer to 2 decimal places.

Given , , and , what is ?

Let be the population vector of a city giving o, the number of people who own their home and r, the number of people who rent. Suppose that each year, 3% of the people who own their home move to a rental and 11% of the people who rent purchase a home and become owners. Let be such that . What is ?

In the figure below, the angle between the x-axis and the vector is ______ . Round to the nearest whole number.

Does point in the same direction as the opposite direction, or neither?

How many ft-lbs of work are required to lift a 324 pound refrigerator 8 inches straight up? Round to 2 decimal places.

An airplane is flying at an airspeed of 690 km/hr in a crosswind blowing from the southeast at a speed of 45 km/hr. To end up going due west, the plane should head _____ south of west and will have a speed of ______km/hr relative to the ground. Round each answer to 2 decimal places.

Let the student vector be the number of ninth, tenth, eleventh, and twelfth graders in a high school. If the number of students in each grade doubles, what is the new student vector ?

The angle between the vectors and is _____ . Round to the nearest whole number.

A cyclist goes at 7 mph due north and feels the wind coming against him at a relative velocity of 5 mph due west. The actual velocity of the wind is _____ mph at an angle of ______ west of north. Round both answers to 1 decimal place.

Let , , and . What is ?

Simplify the following:

A man leaves his car and walks 2 miles northeast, 4 miles east, and then 8 miles southwest. How far is the person from his car? In what direction must he walk to head directly to his car?

For and , what is ?

A man is sitting 9 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 5 meters directly north of the fence corner. How far is the man from the bird? Round your answer to 3 decimal places.

For what value of x do and have the same length?

A horse runs at a constant speed of 16 m/sec. He starts at a fence and his path makes an angle of with the fence. After 11 seconds, how far is he from the fence?

If and , find .

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 . Let be the population vector (in tens of thousands) in the year 2005. What is ?