A standard gold bar stored at Fort Knox, Kentucky, is 7.00 inches long, 3.63 inches wide, and 1.75 inches tall. Gold has a density of $19,300 \mathrm { kg } / \mathrm { m } ^ { 3 }$. What is the mass of such a gold?

The deepest point in the ocean is 11 km below sea level, deeper than MT. Everest is tall. What is the pressure in atmospheres at this depth?

A tall cylinder contains 25 cm of water. Oil is carefully poured into the cylinder, where it floats on top of the water, until the total liquid depth is 40 cm. What is the gauge pressure at the bottom of the cylinder?

A large amount of the gold reserve for the United States is stored in the Fort Knox Bullion Depository vault in Kentucky. Much of it is in the form of bars with the dimensions 7 in x 3 5/8 in x 1 3/4 in. The gold has a density of 19,300 kg/m^3. Calculate the mass of one gold bar (1 in = 2.54 cm). If you picked up this gold bar, would it be more like picking up a can of soda, a gallon of water, or a box of books?

A 100 mL beaker holds 120 g of liquid. What is the liquid's density in SI units?

A beaker of water rests on a scale. A metal ball is then lowered into the beaker using a string tied to the ball. The ball doesn't touch the sides or bottom of the beaker, and no water spills from the beaker. Does the scale reading decrease, increase, or stay the same? Explain.

The magnitude of the force vector

$$\vec { \mathbf { F } }$$

is 82.3 newtons. The x component of this vector is directed along the +x axis and has a magnitude of 74.6 newtons. The y component points along the +y axis. (a) Find the direction of

$$\vec { \mathbf { F } }$$

relative to the + x axis. (b) Find the component of

$$\vec { \mathbf { F } }$$

along the +y axis.

Evaluate $\iint_{S} \mathbf{F} \cdot \mathbf{N} d s$ for vector field $\mathbf{F}$, where $\mathbf{N}$ is an outward normal vector to surface S. $\mathbf{F}(x, y, z)=x \mathbf{i}+2 y \mathbf{j}=3 z \mathbf{k}$, and S is that part of plane 15x-12y+3z=6 that lies above unit square $0 \leq x \leq 1,0 \leq y \leq 1$.

A board is 6 feet long. How many 2/3-foot-long pieces can be cut from the board? Use the number line to show your work.

Why is the number of pieces that can be cut from the board greater than the number of feet in the length of the board?

The deepest point in the ocean is 11 km below sea level, deeper than Mt. Everest is tall. What is the pressure in atmospheres at this depth?

You are looking for a deep spot to take a swim in a local river. The width of the river is about the same all along its length, but there are places where the water flows quickly and places where it flows slowly. Which is a better choice for a swim?

To explore the bottom of a 10-m-deep lake, your friend Tom proposes to get along garden hose, put one end on land and the other in his mouth for breathing underwater, and descend into the depths. Susan, who overhears the conversation, reacts with horror and warns Tom that he will no the be able to inhale when he is at the lake bottom. Why is Susan so worried?

In ΔUVW, the measure of ∠W=90°, WV = 77, VU = 85, and UW = 36. What ratio represents the sine of ∠V?

Scuba divers are warned that if they must make a rapid ascent, they should exhale on the way up. If a diver rapidly ascends to the surface with lungs full of air, his lungs could be damaged. Explain why this is so.