How does modern relativity modify the law of conservation of momentum?

What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected result?

Suppose you measure the terminal voltage of a 1.585-V alkaline cell having an internal resistance of $0.100 \Omega$ by placing a $1.00-\mathrm{k} \Omega$ voltmeter across its terminals. (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

(a) How could you travel far into the future of Earth without aging significantly? (b) Could this method also allow you to travel into the past?

(a) Does motion affect the rate of a clock as measured by an observer moving with it? (b) Does motion affect how an observer moving relative to a clock

measures its rate?

The coating on the inside of fluorescent light tubes absorbs ultraviolet light and subsequently emits visible light. An inventor claims that he is able to do the reverse process. Is the inventor’s claim possible?

When you are flying in a commercial jet, it may appear to you that the airplane is stationary and Earth is moving beneath you. Is this point of view valid? Discuss briefly.

Calculate the dot product $\mathbf{u} \cdot \mathbf{v}$.

$$\mathbf{u}=\left[\begin{array}{l} 1 \\ 3 \end{array}\right], \ \mathbf{v}=\left[\begin{array}{r} 4 \\ -2 \end{array}\right]$$

Which value of $\Delta G$ corresponds with $K_{\mathrm{eq}}<1$? (a) +1 kj/mol (b) 0 kj/mol (c) -1 kj/mol

What are the advantages and disadvantages of connecting batteries in series? In parallel?

Find the exact value of each expression. Do not use a calculator. $\sin^{-1}\left(\sin \frac{\pi}{5}\right)$

Solve each equation. Check your solution. $\frac{d}{11}=-8$

Draw structures for any five constitutional isomers with the molecular formula $\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}_{3}$.

If $g(x)=-6 x,$ find each function value. $g(-12)$