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Hydraulics is the transmission of force through the use of liquids. Liquids are especially suited for transferring force in complex machines because they compress very little and can occupy very small spaces. Hydraulic pressure is calculated by dividing force by the area over which it is applied: P = F/A where F is force in pounds, A is area in square inches, and the resulting pressure is in pounds per square inch (psi).

Power is the rate at which work is performed or work per unit time:  \(P = {w \over t}\)  and is measured in watts (W).

Wrenches are used with threaded fasteners like bolts and nuts. A bolt has external threads while a nut has internal threads and this thread pattern combination allows them to lock together and act as fasteners. Nuts come in a variety of configurations including wing nuts which provide appendages that allow tightening and loosening by hand, slotted nuts that use a cotter pin to lock the nut in place and prevent it from loosening, and lock nuts that also prevent loosening via nylon in their threads. Threads are identified by pitch which is the number of threads per inch.

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

Because different materials have different refractive indices, light changes speed when passing from one material to another. This causes the light to bend (refraction) at an angle that depends on the change in refractive index between the materials. The greater the difference, the higher the angle of refraction.

To convert from C° to F° use:

\(F° = {9 \over 5}C° + 32\)

\(F° = {9 \over 5}(5) + 32\)

\(F° = {45 \over 5} + 32\)

\(F° = 9 + 32 = 41\)

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{6} \) ÷ \( \frac{4}{8} \) = \( \frac{4}{6} \) x \( \frac{8}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{6} \) x \( \frac{8}{4} \) = \( \frac{4 x 8}{6 x 4} \) = \( \frac{32}{24} \) = 1\(\frac{1}{3}\)