Each of two vectors,  and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is

data-wiris-created="true" class="Wirisformula" />. Which possibility is correct?

A.

 and  both lie along the positive x axis.

B.

 lies along the positive x axis.  lies along the negative x axis.

C.

 and  both lie along the positive y axis.

D.

lies along the negative x axis.  lies along the negative y axis.

E.

lies along the positive y axis.  lies along the negative y axis.

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Answer: D

Physics & Space Science

A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal. What is the forward speed of the disk after it has rolled 3.0 m, measured along the plane?

A) 2.0 m/s B) 3.5 m/s C) 4.1 m/s D) 5.7 m/s E) 6.3 m/s

Explain how we can estimate the geological age of a planetary surface from its number of impact craters

What will be an ideal response?

A 25-L container holds ideal hydrogen (H2) gas at a gauge pressure of 0.25 atm and a temperature of 0°C

What mass of hydrogen gas is in this container? The ATOMIC mass of hydrogen is 1.0 g/mol, the ideal gas constant is R = 8.314 J/mol ? K = 0.0821 L ? atm/mol ? K, and 1.00 atm = 101 kPa. A) 1.4 g B) 2.8 g C) 4.2 g D) 5.6 g E) 6.3 g

A 10.0-kg box starts at rest and slides 6.0 m down a ramp inclined at an angle of 10° with the horizontal. If there is no friction between the ramp surface and crate, what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s2)

a. 6.1 m/s c. 10.7 m/s b. 3.5 m/s d. 4.5 m/s