The mass of one oxygen molecule is $5.3 \times 10^{-23}$ gram. Find the mass of 20,000 molecules of oxygen. Express the answer in scientific notation.

An oxygen molecule consists of two oxygen atoms whose total mass is $5.3 \times 10^{-26} \mathrm{kg}$ and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $1.9 \times 10^{-46} \mathrm{kg} \cdot \mathrm{m}^{2}.$ From these data, estimate the effective distance between the atoms.

True/False. When an object is passed to a method, what is actually passed is a reference to that object.

Ken and Joanne are astronauts floating some distance apart in space. They are joined by a safety cord whose ends are tied around their waists. If Ken starts pulling on the cord, will he pull Joanne toward him, or will he pull himself toward Joanne? Explain what happens.

In the lungs there are tiny sacs of air, which are called alveoli. An oxygen molecule (mass=$5.3 \times 10^{-26}$ kg) is trapped within a sac, and the uncertainty in its position is 0.12 mm. What is the minimum uncertainty in the speed of this oxygen molecule?

Write the number indicated in each statement in scientific notation. (a) The distance from the earth to the sun is about 93 million miles. (b) The mass of an oxygen molecule is about 0.000000000000000000000053 g. (c) The mass of the earth is about 5,970,000,000,000,000,000,000,000 kg.

An oxygen container that one can use in the mountains has a 90-min oxygen supply at a speed of $6 \mathrm{L} / \mathrm{min}$.Determine everything you can about the gas in the container. Make reasonable assumptions.

The mass of one oxygen molecule is $5.3 \times 10^{-23}$ gram. Find the mass of 20,000 molecules of oxygen. Express the answer in scientific notation.

The mass of one oxygen molecule is

$$5.3 \times 10 ^ { - 23 }$$

gram. Find the mass of 20,000 molecules of oxygen. Express the answer in scientific notation.

A mountain climber’s oxygen tank contains 1 lb of oxygen when he begins his trip at sea level where the acceleration of gravity is 32.174 ft/s$^{2}$. What is the weight of the oxygen in the tank when he reaches the top of Mt. Everest where the acceleration of gravity is 32.082 ft/s$^{2}$? Assume that no oxygen has been removed from the tank; it will be used on the descent portion of the climb.

Find the value of each of the following.

$$\sin \left[ \cos ^ { - 1 } \left( - \frac { \sqrt { 3 } } { 2 } \right) \right]$$

Use the variable $u$ for the inside function to express the function

$$y=(5t^2-2)^6$$

as a composite function.

In this problem, we turn to data that do not tend to change linearly. Often we can "linearize" the data by taking the logarithm or exponential of the data and then doing a linear fit as described in this section. (a.) Suppose we have, or suspect, a relationship $y=k x^{m}$. Show that by taking the natural logarithm of this equation we obtain a linear relationship: $Y=K+m X$. Explain the new variables and constant K. (b.) Below are data relating the periods of revolution t (in days) of the six inner planets and their semimajor axis $a\left(in 10^{6} \mathrm{km}\right)$. Kepler conjectured the relationship $t=k a^{m},$ which is very accurate for the correct k and a. You are to "transform" the data as in part a (thus obtaining $T_{i}=\ln t_{1}, \cdots ;$ and do a linear fit to the new data, thus finding k and m. "

$$\begin{matrix} \text{t-data} & \text{87.97} & \text{224.7} & \text{365.26} & \text{686.98} & \text{4,332.59} & \text{10,759.2}\\ \text{a-data} & \text{58} & \text{108} & \text{149} & \text{228} & \text{778} & \text{1,426}\\ \end{matrix}$$

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A ball is kicked into the air from ground level. The height h in meters that the ball reaches at a distance d in meters from the point where it was kicked is given by $h=-2d(d-4)$. The graph of the equation is a parabola. At what distance from the point where it is kicked does the ball reach its maximum height? Explain.