Q: Which equation correctly converts Cartesian coordinates $$(x, y) to $$polar coordinates $$(r, \theta)$$?

$$r = \sqrt{x^2$ + y^2$}$$, $$\theta = \tan$$^{-1}$$(y/x)$$

Q: Which of the following is true about the vector product (cross product) of two vectors?

$$\vec{A} \times \vec{B} = -\vec{B} \times \vec{A}$$

Q: Which coordinate system is most appropriate for describing the position of a point on the surface of a sphere?

Spherical coordinates $$(r, \theta, \phi)$$

Question 1

If you were to eat one French fry per second, estimate how many years it would take you to eat a linear chain of French fries, placed end to end, that reach from the Earth to the Moon (distance = 250,000 miles, average fry length = 0.08 m)?

Accepted Answer

200 years

Question 2

How many significant figures are in the number 0.00320?

Accepted Answer

3

Question 3

When multiplying 13.8 m, 2.05 m, and 0.062 m, how many significant figures should the result have?

Accepted Answer

2

Question 4

Which of the following is the correct result for $$13.8 + 2.05 - 0.062 m$$, rounded to the correct number of significant figures?

Accepted Answer

$$15.8 m$$

Question 5

A vector has components $$A_x = 3$$, $$A_y = 4. $$What is the magnitude $$|\vec{A}|$$?

Accepted Answer

$$5$$

Question 6

Given vectors $$\vec{A} = (0,2,1)$$, $$\vec{B} = (3,0,2)$$, and $$\vec{C} = (1,-4,2)$$, what is $$\vec{D} = \vec{A} + \vec{B} + \vec{C}$$?

Accepted Answer

$$(4, -2, 5)$$

Question 7

Which of the following is a unit vector in the $$x-$$direction?

Accepted Answer

$$\hat{i}$$

Question 8

What is the scalar (dot) product of $$\vec{A} = (2, 3, 0)$$ and $$\vec{B} = (1, -1, 4)$$?

Accepted Answer

$$-1$$

Question 9

Which equation correctly converts Cartesian coordinates $$(x, y) to $$polar coordinates $$(r, 	heta)$$?

Accepted Answer

$$r = \sqrt{x^2$ + y^2$}$$, $$	heta = 	an$$^{-1}$$(y/x)$$

Question 10

The cross product $$\vec{A} 	imes \vec{B} is$$:

Accepted Answer

A vector perpendicular to both $$\vec{A}$$ and $$\vec{B}$$

Question 11

Which of the following statements is true about the scalar (dot) product?

Accepted Answer

It is commutative

Question 12

If $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$0$$

Question 13

Which of the following is the correct formula for the magnitude of the cross product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$|\vec{A}||\vec{B}|\sin\phi$$

Question 14

Which of the following is true about the vector product (cross product) of two vectors?

Accepted Answer

$$\vec{A} 	imes \vec{B} = -\vec{B} 	imes \vec{A}$$

Question 15

A vector $$\vec{R} in 3D $$has components $$R_x = 2$$, $$R_y = -3$$, $$R_z = 6. $$What is $$|\vec{R}|$$?

Accepted Answer

$$\sqrt{2^2$ + (-3)^2$ + 6^2$}$$

Question 16

Which of the following is NOT a property of unit vectors?

Accepted Answer

They can have any magnitude

Question 17

If $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = -\hat{i} + 4\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\hat{i} + 7\hat{j}$$

Question 18

Which coordinate system is most appropriate for describing the position of a point on the surface of a sphere?

Accepted Answer

Spherical coordinates $$(r, 	heta, \phi)$$

Question 19

Which of the following is the correct result for $$2.4 - 0.0023$$, rounded to the correct number of significant figures?

Accepted Answer

$$2.4$$

Physics with Calculus: Units, Physical Quantities, and Vectors

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