Prove that L defined in (7) is a linear operator by

College Physics 1
Problem 25PE A projectile is launched at ground level with an initial speed of 50.0 m/s at an angle of 30.0 above the horizontal. It strikes a target above the ground 3.00 seconds later. What are the x and y distances from where the projectile was launched to where it lands?

Classical Mechanics 0
Write down the Lagrangian for a projectile (subject to no air resistance) in terms of its Cartesian coordinates (x, y, z), with z measured vertically upward. Find the three Lagrange equations and show that they are exactly what you would expect for the equations of motion.

Chemistry 11
An iron bar weighed 664 g. After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\). Calculate the final mass of the iron bar and rust.

Chemistry 11
The standard enthalpy change \(\Delta H^{\circ}\) for the thermal decomposition of silver nitrate according to the following equation is +78.67 kJ: \(\mathrm{AgNO}_{3}(s) \rightarrow A g N \mathrm{NO}_{2}(s)+\frac{1}{2} \mathrm{O}_{2}(g)\) The standard enthalpy of formation of \(\mathrm{AgNO}

Psychology 1
Compare and contrast classical and operant conditioning. How are they alike? How do they differ?

Principles of Economics 9
In competitive markets, farmers adopt new technologies that will eventually reduce their revenue because a. each farmer is a price taker. b. farmers are short-sighted. c. regulation requires the use of best practices. d. consumers pressure farmers to lower prices.

Chemistry for today : general, organic, and biochemistry 9
In the reaction \(4 \mathrm{Al}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}\), how many grams of \(\mathrm{O}_{2}\) are needed to completely react with 1.5 moles of Al? a. 24 g b. 36 g c. 48 g d. 60 g

Biochemistry 9
Why is it essential that the mechanisms that activate glycogen synthesis also deactivate glycogen phosphorylase?