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There are seven different Standardised International (SI) units of measurements from which all others are derived. These are:
Name
|
Phenomenon
|
Units
|
metre
|
Length
|
m
|
second
|
time
|
s
|
kilogram
|
mass
|
kg
|
ampere
|
electric current
|
A
|
kelvin
|
thermodynamic temperature
|
K
|
mole
|
Amount of substance
|
mol
|
Luminous intensity
|
candela
|
cd
|
There are 22 derived physical phenomena, shown below. The names, phenomena, units and base units have been mixed up.
Name
|
Phenomenon
|
Units
|
Base units |
becquerel, Bq
|
capacitance
|
A / V
|
$\quad\quad$m$^2$m$^{-2}$cd |
degrees Celsius, $^\circ$ C
|
electric
conductance |
C / V
|
$\quad\quad$K |
coulomb, C
|
electric
potential |
cd sr
|
$\quad\quad$kg s$^{-2}$ A$^{-1}$ |
farad, F
|
electric
resistance |
J / kg
|
$\quad\quad$m kg s$^{-2}$ |
gray, Gy
|
electrical
charge |
J / kg
|
$\quad\quad$m$^{1}$m$^{-1}$ |
henry, H
|
energy
|
J / S
|
$\quad\quad$m$^{2}$ m$^{-4}$ cd |
Hertz, Hz
|
flux of light
|
$\quad\quad\quad$lm / m$^2$ | $\quad\quad$m$^{2}$ kg s$^{-2}$ |
joule, J
|
force
|
$\quad\quad\quad$N / m$^{2}$ | $\quad\quad$m$^{2}$ kg s$^{-2}$ A$^{-1}$ |
katal, kat
|
frequency
|
N m
|
$\quad\quad$m$^{2}$ kg s$^{-2}$ A$^{-2}$ |
lumen, lm
|
illuminance
|
V / A
|
$\quad\quad$m$^{2}$ kg s$^{-3}$ |
lux, lx
|
inductance
|
V s
|
$\quad\quad$m$^{2}$ kg s$^{-3}$ A$^{-1}$ |
newton, N
|
magnetic flux
|
W / A
|
$\quad\quad$m$^{2}$ kg s$^{-3}$ A$^{-2}$ |
ohm, $\Omega$
|
magnetic
flux density |
Wb / A
|
$\quad\quad$m$^{-2}$ kg$^{-1}$ s$^{3}$ A$^{2}$ |
pascal, Pa
|
plane angle
|
$\quad\quad\quad$Wb / m$^2$ | $\quad\quad$m$^{-2}$ kg$^{-1}$ s$^{4}$ A$^{2}$ |
radian, rad
|
power
|
$\quad\quad$m$^{2}$ s$^{-2}$ | |
siemens, S
|
pressure
|
$\quad\quad$m$^{2}$m$^{-2}$ | |
sievert, Sv
|
radiation
dose |
$\quad\quad$sA | |
steradian, sr
|
solid
angle |
$\quad\quad$s$^{-1}$ | |
tesla, T
|
temperature
|
$\quad\quad$s$^{-1}$ mol | |
volt, V
|
unit of catalytic activity
|
||
watt, W
|
|||
weber, Wb
|
(data sourced from the Bureau International des Poids et Mesures http://www.bipm.org/)
Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?
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Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.