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General Science

Which of the following is not a vector quantity?

mass

Velocity and displacement are vector quantities which means each is fully described by both a magnitude and a direction. In contrast, scalar quantities are quantities that are fully described by a magnitude only. A variable indicating a vector quantity will often be shown with an arrow symbol: \(\vec{v}\)

Word Knowledge

Mandate most nearly means:

command

An official order or commission to do something.

Mechanical Comprehension

If the green arrow in this diagram represents 420 ft⋅lb of work, how far will the box move if it weighs 140 pounds?

3 ft.

The Law of Work states that the work put into a machine is equal to the work received from the machine under ideal conditions. In equation form, that's:

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 420 ft⋅lb and the resistance force is 140 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
420 ft⋅lb = 140 lbs. x d_resistance
d_resistance = \( \frac{420ft⋅lb}{140 lbs.} \) = 3 ft.

Automotive Information

When a car engine is running, what provides electrical current to recharge the battery and power the electrical system?

alternator

Once the engine is running, the alternator provides electrical current to recharge the battery and power the electrical system. The alternator is driven by the engine's crankshaft and produces alternating current (AC) which is then fed through a rectifier bridge to convert it to the direct current (DC) required by the electrical system. A voltage regulator controls the output of the alternator to maintain a consistent voltage (approx. 14.5 volts) in the electrical system regardless of load.

Math Knowledge

The dimensions of this cube are height (h) = 5, length (l) = 1, and width (w) = 4. What is the volume?

The volume of a cube is height x length x width:

v = h x l x w
v = 5 x 1 x 4
v = 20

Arithmetic Reasoning

Solve for \( \frac{5!}{6!} \)

\( \frac{1}{6} \)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)

Word Knowledge

Obnoxious most nearly means:

objectionable

Highly offensive.

General Science

The Sun is a __________-type main-sequence star.

The Sun is a G-type main-sequence star (G2V) but is informally known as a yellow dwarf star. Composed of 73% hydrogen and 25% helium, the hot plasma that makes up the Sun reaches 9,900°F (5,505°C) at the surface. It formed approximately 4.6 billion years ago and makes up 99.86% of the mass in the solar system.

Word Knowledge

Pretentious most nearly means:

pompous

Making unjustified claims.

General Science

Which of the following would be found on a reflecting telescope?

concave mirror

A concave (or converging) mirror bulges inward and focuses reflected light on the mirror's focal point where the mirror's angles of incidence converge. In contrast, a convex (or diverging) mirror bulges outward and diffuses the light waves that strike it. A common use of a concave mirror is in a reflecting telescope, a common use of a convex mirror is in the side view mirror of a car.