Verify that the von Klitzing constant, $h / e^2$, gives the SI unit for resistance (the ohm) if $h$ and $e$ are in units of joule-seconds and coulombs, respectively.

(i) Find the

$$x ^ { 5 } y ^ { 7 }$$

term in the expansion of

$$( x + y ) ^ { 12 }$$

. (ii) Find the

$$a ^ { 7 } b ^ { 9 }$$

term in the expansion of

$$( a + b ) ^ { 16 }$$

. (iii) Find the

$$c ^ { 3 } d ^ { 2 }$$

term in the expansion of

$$( c + d ) ^ { 5 }$$

. (iv) Find the

$$a ^ { 2 } b ^ { 7 }$$

term in the expansion of

$$( a + b ) ^ { 9 }$$

. (v) Find the

$$x ^ { 2 } y ^ { 4 }$$

term in the expansion of

$$( x + y ) ^ { 6 }$$

.

The kilowatt-hour (kWh) is a common unit in measurements of the consumption of electri city. What is the conversion factor between the kilowatt-hour and the joule ? Express 15.3 kWh in joules.

Find the value of y for the given value of x. $y=3 x+2 ; x=0.5$

Thomson observed that the production of cathode rays did not depend on the kind of gas in the tube or the type of metal used for the electrodes. What conclusion did he draw from these observations?

A person can survive a feet-first impact at a speed of about $12 \mathrm{~m} / \mathrm{s}(27 \mathrm{mi} / \mathrm{h})$ on concrete, $15 \mathrm{~m} / \mathrm{s}(34 \mathrm{mi} / \mathrm{h})$ on soil, and $34 \mathrm{~m} / \mathrm{s}(76 \mathrm{mi} / \mathrm{h})$ on water. What is the reason for the different values for different surfaces?

Which x-value gives the same value for $Y_1$ and $Y_2$?

Refer to the expansion of $(r+s)^{\mathrm{15}}.$ How many terms are in the expansion?

Indicate whether J.J. Thomson would have agreed or disagreed with each of the following statement. "Atoms of all elements contain electrons." Give reasons for your answer.

Compare the expansion of $(a+b)^n$ with the expansion of $(a-b)^n$. Give an example.

Consider the following models of the atom: (a) Dalton, (b) Thomson, (c) Rutherford. How does the location of the electrons in an atom vary? How does the location of the atom's positive matter compare?

Consider a cold aluminum canned drink that is initially at a uniform temperature of $5^{\circ} \mathrm{C}$. The can is $12.5 \mathrm{~cm}$ high and has a diameter of $6 \mathrm{~cm}$. The emissivity of the outer surface of the can is $0.6$. Disregarding any heat transfer from the bottom surface of the can, Find how long it will take for the average temperature of the drink to rise to $7^{\circ} \mathrm{C}$ if the surrounding air and surfaces are at $25^{\circ} \mathrm{C}$.

In this exercise, complete two iterations of Newton's Method for the function using the given initial guess.

$$f(x)=x^2-3, \quad x_1=1.7$$

Find the binary expansion of an integer from the decimal expansion of this integer, and vice versa.