Because your are so smart in physics and engineering, you decide to make your own temperature scale. You also design

it after your favorite element, mercury. You decree that the boiling temperature of mercury in your temperature scale

is $100N(N$ stands for narcissist, naturally$),$ and that the freezing point of mercury is $0\mathrm{.}00N.$ The boiling point of

mercury is $357C$ and the freezing point is $-39\mathrm{.}0C.$

$($a$)$ Derive an equation that relates your $N$ to $C.$

$($b$)$ Derive an equation that relates your $N$ to $F.$

$($c$)$ What is the boiling point of water in $N?$