What are the rules for ending a sentence with a verb?

All three versions occur, though they don't falute the same.

• (c) is the canonic source, with simple Wh-fronting, leaving is at the end of the sentence:

  does anyone know [the task for the afternoon is what]? ==>

  does anyone know [what the task for the afternoon is]?

• (b) is a further variation on (c), with the prepositional phrase for the afternoon, which modifies task, moved (by the rule of "Extraposition from NP") from right after task to the end of the sentence.

  does anyone know [what the task for the afternoon is]? ==>

  does anyone know [what the task is for the afternoon]?

  In this position, it balances the is. This is an esthetic improvement, not a grammatical one. English doesn't like long complex sentences that end with is (like (c) -- the effect is rather like hearing the first two musical notes of a 3-note chord progression; you keep waiting for the other note to drop.

• (a), on the other hand, is a variant of (c) with Subject/Auxiliary Inversion performed, the same way it would be on a real, non-embedded, information-seeking question. It's not proper written English, but is very common in speech, where it has an additional pragmatic usage to signal that the speaker really does want an answer to the question, and not just a Yes or No. (Notice, by the way, that this also has the effect of keeping the is away from the end of the sentence, which is another reason it occurs so frequently.)

  does anyone know [what the task for the afternoon is]? ==>

  does anyone know [what is the task for the afternoon]? (Tell me, please; I really need to know)

Verbs such as break, sell, and read are examples of what are commonly called ergative verbs. Wikipedia's article on this topic defines an ergative verb as:

... a verb that can be either transitive or intransitive, and whose subject when intransitive corresponds to its direct object when transitive.

There is a comprehensive list of ergative verbs on Wiktionary.

Note, however, that the designation of such verbs as ergative is somewhat problematic. The Oxford Dictionary of English Grammar, for example, states: "Some linguists caution against the use of this term". The Oxford Dictionary of Linguistics is more forthright, stating: "The term could perhaps with benefit be avoided". A related Wikipedia article about ergative-absolute languages refers to such verbs in English as "so-called ergative verbs".

Nevertheless, it is important for English language learners to know that many common verbs behave in this way in English, that this is the term they should search for on the internet, and that pedagogic grammars also use the term. For example, here is what the Collins Cobuild English Grammar (p156) says:

Verbs which can have the same thing as their object, when transitive, or their subject when intransitive, are called ergative verbs. For many students of English, the ergative verb is a new idea, and may take a little time to learn. However, it is an important type of verb, as the common examples below make clear. There are several hundred ergative verbs in regular use in current English.