Final answer:
The statement about foxes using a 'shake and break' method is false, as they usually kill small prey with a bite. The energy statement related to a rock being thrown is also false; potential energy increases with height, not kinetic. Lastly, the mark and recapture method is suitable for mammals and birds, but less so for other organisms.
Step-by-step explanation:
The statement "Foxes use the shake and break method for breaking animals' necks" is false. Foxes have been observed to use various methods to catch and kill prey, depending on the situation and type of prey. However, foxes typically kill smaller prey with a bite to the neck or body, not by shaking to break the neck. The 'shake and break' method is not a typical or primary hunting strategy for foxes. When a fox catches larger prey, it may shake it, but this is done to subdue the prey rather than to break its neck.
In regards to energy and rocks, the statement that throwing a rock into the air increases its kinetic energy is false. When a rock is thrown up, its kinetic energy is converted into potential energy as the height increases. As the rock falls down, the potential energy is then converted back into kinetic energy, not the other way around.
As for the mark and recapture method, it is indeed useful for studying population sizes of various animals including mammals and birds, but it might not be as effective for organisms that are difficult to mark or recapture, such as some aquatic species or insects.