Deck 1: Overview

Question 1

What is the magnitude of the vector ?

A)2.0
B)6.0034
C)7.2
D)10
E)24

Answer 1

7.2

Question 2

Assume that the mass of any cell in the human body is 5 * 10^-15 kg.If Alice has a mass of 50 kg how many cells are there in her body?

A)10¹⁷ cells
B)10¹⁶ cells
C)10¹⁵ cells
D)10¹⁴ cells
E)10¹³ cells

Answer 2

10¹⁶ cells

Question 3

A vector with magnitude 25.0 m points along the negative x direction.If it is rotated by 50.0 degrees counterclockwise,what are the components of the vector?

A)A_x = 25.0 cos 50.0 ^$\circ$ and A_y = 25.0 sin 50.0 ^$\circ$
B)A_x = 25.0 sin 50.0 ^$\circ$ and A_y = 25.0 cos 50.0 ^$\circ$
C)A_x = 25.0 sin 230 ^$\circ$ and A_y = 25.0 cos 230 ^$\circ$
D)A_x = 25.0 cos 230 ^$\circ$ and A_y = 25.0 sin 230 ^$\circ$

Answer 3

A_x = 25.0 cos 230 ^$\circ$ and A_y = 25.0 sin 230 ^$\circ$

Question 4

A vector with magnitude 25.0 m points along the negative y direction.If it is rotated by 50.0 degrees counterclockwise,what are the components of the vector?

A)A_x = 25.0 sin 320 ^$\circ$ and A_y = 25.0 cos 320 ^$\circ$
B)A_x = 25.0 sin 50.0 ^$\circ$ and A_y = 25.0 cos 50.0 ^$\circ$
C)A_x = 25.0 cos 50.0 ^$\circ$ and A_y = 25.0 sin 50.0 ^$\circ$
D)A_x = 25.0 cos 320 ^$\circ$ and A_y = 25.0 sin 320 ^$\circ$

Question 5

and have the same magnitude v.The direction of is north and the direction of is 60 degrees west of south.What is the magnitude of - ?

A)zero
B)v
C)
D)2v

Question 6

What is the minimum number of post-it note sheets,length 3.00 inches and width 2.00 inches,you would need to make a straight line from the wall in your dorm room to the door which is 30.0 feet away from the wall?

A)50
B)80
C)120
D)180
E)200

Question 7

The measured length of a cylindrical laser beam is 12.1 meters,its measured diameter is 0.00121 meters,and its measured intensity is 1.21 * 10⁵ W/m².Which of these measurements is the most precise?

A)length
B)diameter
C)intensity
D)All three are equally precise.

Question 8

A sphere and a cube have the same volume.If the radius of the sphere is 5.00 cm,then what is the area of one side of the cube?

A)25.0 cm²
B)65.0 cm²
C)105 cm²
D)125 cm²

Question 9

A car's gasoline tank has the shape of a right rectangular box and has a square base.Its capacity is 61.0 liters.If there are 45.0 liters of gasoline in the tank and the distance between the top of the tank and the gasoline surface in the tank is 4.30 cm,what is the length of one side of the tank's square base? Assume the car is parked on level ground.

A)3.72 cm
B)102 cm
C)61.0 cm
D)119 cm
E)14.2 cm

Question 10

Approximately how many water molecules are in one liter of water? One mole contains 6.02 * 10²³ molecules,the density of water is 1.00∙10³ grams/liter and the mass of one mole of water is 18.0 grams.

A)6.02 * 10²³
B)3.34 * 10²⁵
C)6.02 * 10²⁶
D)1.08 * 10²⁸

Question 11

A car's gasoline tank has the shape of a right rectangular box having a square base of side 65 cm.Its capacity is 68 liters.If the distance between the top of the tank and the gasoline surface in the tank is 5.60 cm,what volume of gasoline is in the tank? Assume the car is parked on level ground.

A)30.6 liters
B)23.0 liters
C)44.4 liters
D)62.1 liters
E)57.8 liters

Question 12

A vector with magnitude 25.0 m points along the positive x direction.If it is rotated by 50.0 degrees counterclockwise,what are the components of the vector?

A)A_x = 25.0 sin 50.0 ^$\circ$ and A_y = 25.0 cos 50.0 ^$\circ$
B)A_x = 25.0 cos 50.0 ^$\circ$ and A_y = 25.0 sin 50.0 ^$\circ$
C)A_x = 25.0 sin 310 ^$\circ$ and A_y = 25.0 cos 310 ^$\circ$
D)A_x = 25.0 cos 310 ^$\circ$ and A_y = 25.0 sin 310 ^$\circ$

Question 13

A vector with magnitude 25.0 m points along the positive y direction.If it is rotated by 50.0 degrees counterclockwise,what are the components of the vector?

A)A_x = 25.0 cos 50.0 ^$\circ$ and A_y = 25.0 sin 50.0 ^$\circ$
B)A_x = 25.0 cos 140 ^$\circ$ and A_y = 25.0 sin 140 ^$\circ$
C)A_x = 25.0 sin 140 ^$\circ$ and A_y = 25.0 cos 140 ^$\circ$
D)A_x = 25.0 tan 50.0 ^$\circ$ and A_y = 25.0 sin 50.0 ^$\circ$

Question 14

A sphere and a cube have the same volume.If the the edge of one side of the cube is 5.00 cm,then what is the surface area of the sphere?

A)25.0 cm²
B)121 cm²
C)150.0 cm²
D)105 cm²

Question 15

A farmer has a field which is 0.50 km in length and 0.70 km in width.What is the area of his field?

A)0.35 km²
B)3.5 km²
C)35 km²
D)3.5 * 10² km²

Question 16

The surface area of a window pane of length 20.5 cm and width 11.9 cm is (given in scientific notation and with the correct number of significant figures):

A)2.4395 * 10² cm²
B)2.440 * 10² cm²
C)2.44 * 10² cm²
D)2.4 * 10² cm²
E)2.0 * 10² cm²

Question 17

How many significant figures are in the number 0.00640?

A)1
B)2
C)3
D)4
E)5

Question 18

and have the same non-zero magnitude.The magnitude of + is equal to the magnitude of - .What is the angle between and ?

A)30 degrees
B)45 degrees
C)60 degrees
D)90 degrees

Question 19

The volume of a rectangular block of width w = 116.5 cm,depth d = 164.8 cm,and height h = 105.1 cm is (given in scientific notation and with the correct number of significant figures):

A)2.018 * 10⁶ cm³
B)2.02 * 10⁶ cm³
C)2.0178 * 10⁶ cm³
D)2.0 * 10⁶ cm³
E)2.01784 * 10⁶ cm³

Question 20

A car's gasoline tank has the shape of a right rectangular box having a square base of side 62 cm.Its capacity is 56 liters.If there are 50 liters of gasoline in the tank,what is the distance between the top of the tank and the gasoline surface in the tank? Assume the car is parked on level ground.

A)14.6 cm
B)13.0 cm
C)22.5 cm
D)1.56 cm
E)33.5 cm

Question 21

The answer with the correct number of significant figures to the following calculation: 1.345 * 6.72 + 4.51 is

A)13.5484.
B)13.548.
C)13.55.
D)13.6.
E)14

Question 22

What is the volume of a box that has dimensions 3.50 cm * 1.000 cm * 4.000 cm?

A)49.0 cm
B)14 cm³
C)14.0 cm³
D)14.00 cm³

Question 23

Given two vectors, and : What is the magnitude of the vector ?

A)15.3
B)17.6
C)18.8
D)19.0
E)20.0

Question 24

If vector and vector ,where and are the units vectors along the x and the y directions respectively.If ,calculate the angle vector makes with respect to the +x axes.

A)-84º
B)-96º
C)84º
D)96º
E)-6º

Question 25

If A = 17.0079,B = 2.05,and C = 3.1415926,then what is A/B + C?

A)11.
B)11.4
C)11.44
D)11.438

Question 26

What is the sum of the polar vectors (13;65 ^$\circ$ )and (21;135 ^$\circ$ )?

A)(21.5;23.3 ^$\circ$ )
B)(28.2;109.4 ^$\circ$ )
C)(14.3;43.2 ^$\circ$ )
D)(25.4;-24.3 ^$\circ$ )
E)(12.2;124.2 ^$\circ$ )

Question 27

Three vectors are all in the same plane,they have equal magnitudes and make 120 ^$\circ$ angles with each other.We can say that

A)the magnitude of their resultant is three times the magnitude of each component vector.
B)the magnitude of their resultant is more than three times the magnitude of each component vector.
C)the magnitude of their resultant is one-third the magnitude of the component vectors.
D)the magnitude of their resultant is zero.
E)the magnitude of their resultant is equal to the magnitude of the component vectors.

Question 28

The radius of the Earth is 6.38 * 10⁶ m.The Earth's radius in miles is

A)27000 miles.
B)10200 miles.
C)24900 miles.
D)7940 miles.
E)3970 miles.

Question 29

An American football receiver starts at the 20 yard-line,15 yards to the right of the quarterback.He runs 10 yards forward and then turns to the right and runs 10 yards before catching the ball thrown by the quarterback.If the quarterback is standing on the 15yard-line,how far must he throw the ball?

A)16 yards
B)29 yards
C)31 yards
D)40 yards

Question 30

A spherical balloon has a radius of 20 cm.It starts losing air and its radius shrinks at a rate of 1 cm/s.What is the rate of change of the balloon's volume when its radius reaches 5 cm?

A)-3.14 * 10^-4 m³/s
B)-3.14 m³/s
C)-1 * 10^-4 m³/s
D)-5 * 10^-4 m³/s
E)-3.14 * 10^-2 m³/s

Question 31

The number of square meters in a square mile is

A)2.60 m².
B)2.60 * 10⁵ m².
C)1.61 * 10³ m².
D)2.60 * 10⁶ m².
E)1.61 * 10⁶ m².

Question 32

A man walks 15 m due east,then makes a sharp left turn and walks 23 m due north and then climbs up a vertical ladder to the top of 6 m high structure.Calculate the total displacement of the man.

A)36 m
B)44 m
C)28 m
D)33 m
E)None are correct.

Question 33

What is the magnitude and direction (with respect to the positive x axis)of the vector ?

A)4.61 @ 36.7 ^$\circ$
B)4.6 @ -37 ^$\circ$
C)4.6 @ 37 ^$\circ$
D)4.6 @ 143 ^$\circ$

Question 34

If vector and vector ,where and are the units vectors along the x and the y directions respectively,calculate the magnitude of vector .

A)10.3
B)17.4
C)-6.7
D)26
E)-12.3

Question 35

Given that the formula for Newtonian gravitation is F = Gm₁m₂/r²,where F is the force,m₁ and m₂ are masses,and r is a unit of length,what are the units for the gravitational constant G?

A)kg³/(ms²)
B)(m/kg)(m/s)²
C)kg m/s²
D)kg²/m²

Question 36

What are the polar coordinates of the vector 3i-2j?

A)(3.6;33.7 ^$\circ$ )
B)(3.6;146.3 ^$\circ$ )
C)(4.2;33.7 ^$\circ$ )
D)(4.2;-33.7 ^$\circ$ )
E)(3.6;-33.7 ^$\circ$ )

Question 37

The number of centimeters in 2.50 miles is

A)4.02 * 10⁵ cm.
B)1.56 * 10⁵ cm.
C)4.02 * 10³ cm.
D)2.54 * 10⁴ cm.
E)8.95 * 10⁶ cm.

Question 38

If you head at a compass heading of 15 ^$\circ$ for 25 m,then go on a heading of 280 ^$\circ$ for 18 m,how far are you from your starting point?

A)15 m
B)29 m
C)32 m
D)38 m

Question 39

Express the polar vector (22;124 ^$\circ$ )in unit vector notation.

A)18.2i - 12.3j
B)-12.3i + 18.2j
C)12.3i - 18.2j
D)12.3i + 18.2j
E)-18.2i + 12.3j

Question 40

The distance to the Sun is one hundred fifty billion meters,which in scientific notation can be written as

A)150 * 10⁹ m.
B)1.50 * 10⁶ m.
C)1.50 * 10¹¹ m.
D)15 * 10¹⁰ m.
E)1.5 * 10¹⁰ m.

Question 41

Given two vectors and vector ,that also lies in the xy plane,have the property A = B but .The vector is

A) .
B) .
C) .
D)All are correct.

Question 42

The speed limit on your street is 35 mi/hr.What is this speed in m/s?

A)16 m/s
B)22 m/s
C)56 m/s
D)78 m/s

Question 43

The sides of a rectangle are measured to have lengths 0.234 cm and 12.78 cm.Find the area of the rectangle using the correct number of significant figures.

A)2.99052 cm²
B)2.9905 cm²
C)2.991 cm²
D)2.990 cm²
E)2.99 cm²

Question 44

A string with a length of 13.1 m is tightly tied between two trees.The second tree is some distance east and north of the first tree.If the second tree is 9.8 m east of the first tree,how far north of the first tree is the second tree?

A)3.3 m
B)6.6 m
C)8.7 m
D)11.5 m
E)22.9 m

Question 45

The width of the nail of you thumb is approximately equal to which of the following units:

A)1 $\mu$ m.
B)1 mm.
C)1 cm.
D)1 m.
E)1 km.

Question 46

The fraction of a kilogram in a milligram is

A)10^-6.
B)10^-4.
C)10^-3.
D)10^-2.

Question 47

What is the sum of the lengths of all the edges of a cube whose volume is 3.97 m³?

A)4.53 m
B)9.50 m
C)12.67 m
D)19.00 m

Question 48

Vector has length 15.2 m and is directed along the x-axis.Vector has length 23.0 m and is directed along the y-axis.Vector has length 6.3 m and is directed along the -y axis.What is the length of the vector ?

A)18.4 m
B)22.4 m
C)24.7 m
D)28.3 m
E)33.0 m

Question 49

The fraction of a square kilometer in a square millimeter is

A)10^-12.
B)10^-9.
C)10^-3.
D)10^-6.

Question 50

The fraction of a cubic kilometer in a cubic millimeter is

A)10^-12.
B)10^-6.
C)10^-9.
D)10^-18.

Question 51

A driver from Canada enters the U.S.The posted speed limit is 45 mph.What is this posted speed limit in km/h?

A)31
B)45
C)53
D)67
E)72

Question 52

The solution of (3.75 * 10^-9)- (6.21 *10^-10)in scientific notation is

A)1.92 * 10^-9.
B)3.13 * 10^-9.
C)4.83 * 10^-10.
D)3.74 * 10^-9.

Question 53

27500 people live in the Duchy of Grand Fenwick,which has a land area of a square 5.8 km on each side.How many people live there per square km?

A)820
B)817
C)810
D)809

Question 54

A gardener wants to build a circular fence around his vegetable garden.If he has 100 feet (1 ft = 0.3048 m)of wire,what is the maximum area covered?

A)0.0000739 km²
B)0.002342 km²
C)23.4 km²
D)75.2 km²
E)81.99 km²

Question 55

The vector = (A_x ,A_y)= ( +7.07 m,+7.07 m)and the vector = (B_x ,B_y)= ( +5.00 m,+8.66 m).What is the magnitude of the angle between the vectors and ?

A)15 ^$\circ$
B)30 ^$\circ$
C)45 ^$\circ$
D)60 ^$\circ$
E)75 ^$\circ$

Question 56

A bicycle tire is inflated to a pressure of 93 psi.What is a pressure of 93 psi in the SI unit pascals (Pa)?

A)6.4 * 10¹ Pa
B)1.6 * 10² Pa
C)1.6 * 10⁴ Pa
D)3.2 * 10⁴ Pa
E)6.4 * 10⁵ Pa

Question 57

What is the ratio of the Earth's density to that of Venus? Their radii are 6378 km and 6051 km,and their masses 5.97 *10²⁴ kg and 4.87 * 10²⁴ kg,respectively.

A)0.96
B)1.05
C)1.16
D)1.44

Question 58

Kobe Bryant of the LAL (LA Lakers)is 6'6" tall.His height in meters is

A)6.2 m.
B)3.5 m.
C)2.9 m.
D)1.98 m.

Question 59

A CD that is 0.75 mm thick has outer diameter of 128 mm and inner diameter of 15 mm.The volume of the CD is

A)1920 mm³.
B)5300 mm³.
C)9520 mm³.
D)38079 mm³.

Question 60

A right cylinder has a cross sectional area of 25.0 cm² and a height of 50.0 cm.What is the volume of the cylinder in SI units?

A)0.000125 m³
B)0.00125 m³
C)0.0125 m³
D)0.125 m³
E)1.250 m³

Question 61

Vector has a length of 5 and an angle of 30 ^$\circ$ with respect to the positive x-axis.Vector has a length of 5 and an angle of 150 with respect to the positive x-axis.What is the angle with respect to the positive x-axis for the vector ?

A)90 ^$\circ$
B)0 ^$\circ$
C)135 ^$\circ$
D)180 ^$\circ$
E)30 ^$\circ$

Question 62

Vector points along the y axis with length 5.0,vector makes an angle of 55 ^$\circ$ with respect to the x-axis and has a length of 7.0.What is the length of vector ?

A)8.6
B)15.
C)11.
D)12.
E)9.3

Question 63

Vector points along the y axis with length 5.0,vector makes an angle of 55 ^$\circ$ with respect to the x-axis and has a length of 7.0.What is the length of vector ?

A)4.1
B)12.
C)2.0
D)35.
E)9.9

Question 64

Vector has a length of 5 and an angle of 30 ^$\circ$ with respect to the positive x-axis.Vector has a length of 5 and an angle of 150 ^$\circ$ with respect to the positive x-axis.What is the angle with respect to the positive x-axis for the vector ?

A)90 ^$\circ$
B)180 ^$\circ$
C)135 ^$\circ$
D)30 ^$\circ$
E)0 ^$\circ$