91Ó°ÊÓ

Evaluate:\(8 \times 2 \div 4 \div 2\)

Evaluate:\(3+4^{2}\)

Evaluate:\(3+4 \times 5^{2}\)

Evaluate:\(25+144^{1 / 2}\)

Evaluate:\(\left(5^{2}+12^{2}\right)^{1 / 2}\)

Find the sum and product of the pairs of complex numbers:\(z_{1}=3+5 i, z_{2}=4-7 i\)

Find the sum and product of the pairs of complex numbers:\(z_{1}=1-6 i, z_{2}=-5-4 i\)

Given that 1 mile \((\mathrm{mi})\) is \(1760 \mathrm{yd}\) and 1 hour (h) is \(60 \mathrm{~min}\), express a speed of 60 miles per hour in (i) \(\mathrm{m} \mathrm{s}^{-1}\), (ii) \(\mathrm{km} \mathrm{h}^{-1}\).

(i) What is the unit of velocity in a system in which the unit of length is the inch (in= \(2.54 \times 10^{-2} \mathrm{~m}\) ) and the unit of time is the hour (h)? (ii) Express this in terms of base SI units. (iii) A snail travels at speed \(1.2\) in \(\min ^{-1}\). Express this in units \(y \mathrm{~d} \mathrm{~h}^{-1}, \mathrm{~m} \mathrm{~s}^{-1}\), and \(\mathrm{km} \mathrm{h}^{-1}\).

The non-SI unit of mass called the (international avoirdupois) pound has value \(1 \mathrm{lb}=0.45359237 \mathrm{~kg}\). The 'weight' of the mass in the presence of gravity is called the pound-force, Ibf. Assuming that the acceleration of gravity is \(g=9.80665 \mathrm{~m} \mathrm{~s}^{-2}\), (i) express \(1 \mathrm{lbf}\) in SI units, (ii) express, in SI units, the pressure that is denoted (in some parts of the world) by \(\mathrm{psi}=1 \mathrm{lbf} \mathrm{in}^{-2}\), (iii) calculate the work done (in SI units) in moving a body of mass \(200 \mathrm{lb}\) through distance \(5 \mathrm{yd}\) against the force of gravity.