Suominen

MATH 104 Name________________________________
Suominen
Test 2
You may use your course notes to solve the problems. However, you may not use any other resources.
Recall by the Academic Integrity Policy, you agree to the following Honor Code:
• Rely solely on your own work.
• Refrain from any activity that would dishonestly or fraudulently improve your results.
• Do not let anyone else complete your test nor attempt to complete any other student’s test.
By submitting this exam, you are acknowledging that you have followed the Honor Code.
Show all your work to receive full credit. Good luck!
1. Use the vector = [
6
−2
] to calculate T() for each of the following transformation.
a) (6 pts) Reflect over the line = .
b) (6 pts) Vertical Shear by a factor of 0.5.
2. (8 pts) Use a composition of transformations to rotate 45° counterclockwise around point (-1, 2) the
vector = [
−4
3
].
3. (6 pts each) Write a matrix that will transform the original image into the transformed image.
a) Original Image: Transformed Image:
b) Original Image: Transformed Image:
4. (8 pts) Suppose “W” is written in regular 12-point font. Write a matrix that will transform “W”
into the italics letter on the right.
Original Letter: Transformed Image:
5. (6 pts each) A jar contains 3 red, 4 green, and 4 clear marbles. Assume the marbles are not replaced
in the jar as each marble is selected.
a. How many different ways can 3 marbles be selected from the jar?
b. What is the probability of selecting a red marble or a clear marble?
6. Use the given graph to answer the following questions:
a) (2 pts) What is the degree of vertex A?
b) (6 pts) Write a Euler path from the graph. If a Euler path does
not exist, explain why.
c) (6 pts) Write a Euler circuit from the graph. If a Euler circuit does not exist, explain why.
d) (6 pts) Write a Hamilton circuit from the graph.
e) (6 pts) Write the adjacency matrix.
f) (6 pts) Write the incidence matrix.
7. (6 pts) Draw a binary tree with 6 leaves and a height of 3.
8. (10 pts) Using quaternions, rotate point (4, 3, 2) 90° about the -axis.