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A nonuniform, 80.0-g, meterstick balances when the support is placed at the 51.0-cm mark. At what location on the meterstick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark?


A) 16.0 cm
B) 67.0 cm
C) 66.0 cm
D) 35.0 cm
E) 34.0 cm

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A record is dropped vertically onto a freely rotating (undriven) turntable. Frictional forces act to bring the record and turntable to a common angular speed. If the rotational inertia of the record is 0.54 times that of the turntable, what percentage of the initial kinetic energy is lost?


A) 35%
B) 18%
C) 46%
D) 60%

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A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal. After it has rolled 4.20 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?


A) 9.80 m/s2
B) 4.60 m/s2
C) 3.29 m/s2
D) 3.07 m/s2
E) 2.30 m/s2

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A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square   on a side and its mass is   what is the magnitude of the horizontal force that the wall at P experiences?   A)  20 N B)  0.00 N C)  7.8 N D)  98 N on a side and its mass is A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square   on a side and its mass is   what is the magnitude of the horizontal force that the wall at P experiences?   A)  20 N B)  0.00 N C)  7.8 N D)  98 N what is the magnitude of the horizontal force that the wall at P experiences? A uniform sign is supported against a wall at point P as shown in the figure. If the sign is a square   on a side and its mass is   what is the magnitude of the horizontal force that the wall at P experiences?   A)  20 N B)  0.00 N C)  7.8 N D)  98 N


A) 20 N
B) 0.00 N
C) 7.8 N
D) 98 N

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In the figure, a weightlifter's barbell consists of two identical uniform spherical masses each with radius 0.17 m and mass of 50 kg. The weights are connected by a 0.96-m uniform steel rod with a mass of 12 kg. Find the moment of inertia of the barbell about the axis through the center (see figure). In the figure, a weightlifter's barbell consists of two identical uniform spherical masses each with radius 0.17 m and mass of 50 kg. The weights are connected by a 0.96-m uniform steel rod with a mass of 12 kg. Find the moment of inertia of the barbell about the axis through the center (see figure).

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A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 0.50 m, causing the disk to accelerate at A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 0.50 m, causing the disk to accelerate at   What is the mass of the disk? A)  17 kg B)  13 kg C)  8.5 kg D)  4.3 kg What is the mass of the disk?


A) 17 kg
B) 13 kg
C) 8.5 kg
D) 4.3 kg

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A uniform piece of wire, 20 cm long, is bent in a right angle in the center to give it an L-shape. How far from the bend is the center of mass of the bent wire?


A) 2.5 cm
B) 3.5 cm
C) 4.5 cm
D) 5.0 cm
E) 7.1 cm

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A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up a ramp that rises at 30.0° above the horizontal. The speed of the ball at the base of the ramp is 2.63 m/s. While the ball is moving up the ramp, find (a) the acceleration (magnitude and direction) of its center of mass and (b) the friction force (magnitude and direction) acting on it due to the surface of the ramp.

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(a) 2.94 m...

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The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2 from the axis of rotation (right) . You release the hanging blocks simultaneously from rest, and call tL the time taken by the block on the left and tR the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2 from the axis of rotation (right) . You release the hanging blocks simultaneously from rest, and call t<sub>L</sub> the time taken by the block on the left and t<sub>R</sub> the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions   A)  t<sub>L</sub> =   t<sub>R</sub>. B)  t<sub>L</sub> = t<sub>R</sub>. C)  t<sub>L</sub> =   t<sub>R</sub>. D)  t<sub>L</sub> = 2t<sub>R</sub>. E)  t<sub>l</sub> = 4t<sub>R</sub>.


A) tL = The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2 from the axis of rotation (right) . You release the hanging blocks simultaneously from rest, and call t<sub>L</sub> the time taken by the block on the left and t<sub>R</sub> the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions   A)  t<sub>L</sub> =   t<sub>R</sub>. B)  t<sub>L</sub> = t<sub>R</sub>. C)  t<sub>L</sub> =   t<sub>R</sub>. D)  t<sub>L</sub> = 2t<sub>R</sub>. E)  t<sub>l</sub> = 4t<sub>R</sub>. tR.
B) tL = tR.
C) tL = The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left) , or a distance r/2 from the axis of rotation (right) . You release the hanging blocks simultaneously from rest, and call t<sub>L</sub> the time taken by the block on the left and t<sub>R</sub> the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions   A)  t<sub>L</sub> =   t<sub>R</sub>. B)  t<sub>L</sub> = t<sub>R</sub>. C)  t<sub>L</sub> =   t<sub>R</sub>. D)  t<sub>L</sub> = 2t<sub>R</sub>. E)  t<sub>l</sub> = 4t<sub>R</sub>. tR.
D) tL = 2tR.
E) tl = 4tR.

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The angular momentum of a system remains constant


A) when the total kinetic energy is constant.
B) when no net external force acts on the system.
C) when the linear momentum and the energy are constant.
D) when no torque acts on the system.
E) all the time since it is a conserved quantity.

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What is the vector product of What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  = 2.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  + 3.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  + 1.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  and What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  = 1.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 3.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 2.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  ?


A) -3.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  + 5.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 9.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00
B) -5.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  + 2.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 6.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00
C) -9.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 3.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 3.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00
D) -4.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  + 3.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 1.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00
E) 2.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  -9.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00  - 2.00 What is the vector product of   = 2.00   + 3.00   + 1.00   and   = 1.00   - 3.00   - 2.00   ? A)  -3.00   + 5.00   - 9.00   B)  -5.00   + 2.00   - 6.00   C)  -9.00   - 3.00   - 3.00   D)  -4.00   + 3.00   - 1.00   E)  2.00   -9.00   - 2.00

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A uniform 300-kg beam, 6.00 m long, is freely pivoted at P, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.00 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 23,000 N in the strut is permitted, due to safety. Under maximum load, find the magnitude of the x component of the force exerted on the beam by the pivot at P. A uniform 300-kg beam, 6.00 m long, is freely pivoted at P, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.00 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 23,000 N in the strut is permitted, due to safety. Under maximum load, find the magnitude of the x component of the force exerted on the beam by the pivot at P.   A)  13,800 N B)  12,800 N C)  11,200 N D)  14,400 N E)  16,000 N


A) 13,800 N
B) 12,800 N
C) 11,200 N
D) 14,400 N
E) 16,000 N

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A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m2. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure) . The percent of the initial kinetic energy of the system that is lost during the capture of the ball is closest to A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m<sup>2</sup>. The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings. A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure) . The percent of the initial kinetic energy of the system that is lost during the capture of the ball is closest to   A)  45%. B)  51%. C)  55%. D)  60%. E)  65%.


A) 45%.
B) 51%.
C) 55%.
D) 60%.
E) 65%.

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A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 rev/s, it stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is closest to


A) 0.00593 N ∙ m.
B) 0.0372 N ∙ m.
C) 0.0466 N ∙ m.
D) 0.0620 N ∙ m.
E) 0.149 N ∙ m.

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An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board (a) by pillar A. (b) by pillar B. An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board (a) by pillar A. (b) by pillar B.

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(a) 1.71 k...

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There must be equal amounts of mass on both side of the center of mass of an object.


A) True
B) False

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A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses.


A) It is impossible to say without knowing the masses.
B) It is impossible to say without knowing the distances.
C) The side the boy is sitting on will tilt downward.
D) Nothing will happen; the seesaw will still be balanced.
E) The side the girl is sitting on will tilt downward.

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If the torque on an object adds up to zero


A) the forces on it also add up to zero.
B) the object is at rest.
C) the object cannot be turning.
D) the object could be accelerating linearly but it could not be turning.
E) the object could be both turning and accelerating linearly.

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A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder? A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder?   A)  538 N B)  706 N C)  1290 N D)  833 N E)  601 N


A) 538 N
B) 706 N
C) 1290 N
D) 833 N
E) 601 N

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If If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  = -4 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  - 2 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  - 3 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  , what is If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  × If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  ?


A) +3 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  - 4 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4
B) +3 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  + 4 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4
C) -3 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  + 4 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4
D) +3 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  + 2 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  - 4 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4
E) -3 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  - 2 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4  + 4 If   = -4   - 2   - 3   , what is   ×   ? A)  +3   - 4   B)  +3   + 4   C)  -3   + 4   D)  +3   + 2   - 4   E)  -3   - 2   + 4

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