Convert \(25\,{}^\circ\mathrm{C}\) to Fahrenheit.

Convert \(68\,{}^\circ\mathrm{F}\) to Celsius.

A temperature changes by \(15\,\mathrm{C^\circ}\). What is this interval in Fahrenheit degrees?

A temperature changes by \(27\,\mathrm{F^\circ}\). What is this interval in Celsius degrees?

Convert \(-22\,{}^\circ\mathrm{F}\) to Celsius.

A sample warms from \(12\,{}^\circ\mathrm{C}\) to \(47\,{}^\circ\mathrm{C}\). Find the initial and final temperatures in Fahrenheit and the temperature change in Fahrenheit degrees.

At what temperature do the Celsius and Fahrenheit scales have the same numerical reading?

A thermometer scale \(X\) is linear. It reads \(10\,{}^\circ\mathrm{X}\) at \(0\,{}^\circ\mathrm{C}\) and \(90\,{}^\circ\mathrm{X}\) at \(100\,{}^\circ\mathrm{C}\). Derive \(T_X\) in terms of \(T_C\).

A weather report says the temperature rose from \(41\,{}^\circ\mathrm{F}\) to \(59\,{}^\circ\mathrm{F}\). Find the temperature change in Celsius degrees and the final temperature in Celsius.

A proposed scale \(Y\) has equal degree size to the Celsius scale but reads \(125\,{}^\circ\mathrm{Y}\) at \(100\,{}^\circ\mathrm{C}\). Derive the conversion between \(Y\) and Celsius, then find the \(Y\) reading at \(-40\,{}^\circ\mathrm{C}\).