I have read a syntax book cover to cover and it seems to stubbornly avoid diagramming sentences with "to be" (or other auxilliary verbs) functioning as the principal verb. For example:
That dog is friendly.
If I want to turn that into a wh-question, I am uncertain of how the movement would be diagrammed.
How friendly is that dog?
As far as I can tell, "is friendly" is a simple tenseness verb phrase. However since "is" also functions as an auxilliary verb, I am assuming that is why it undergoes movement as well. "How" is moved to the head of the complementizer phrase, and takes "friendly" along with it as part of a wh-island. "Is," functioning as both a primary and auxilliary verb, moves into the complementizer position modifying the determiner phrase "that dog." The tense phrase "is friendly" seems to be stuck on the right side unless we are simply dismantling that phrase and moving its components to other roles. That seems somewhat arbitrary to me.
Am I mis-characterizing "is" here by calling it a complementizer? Is that movement just a special case of principal auxilliary verbs in wh-questions?
IANAL (I am not a linguist), so I hope that makes sense.
Edit: this was too long for a response to Bill--
But "friendly" is not an object, right? Unless an AP/A' falls into a similar structural position as a "non-subject."
The main point that confuses me is that "is" is a main verb. Main verbs do not typically undergo movement in English. Think of "That dog is running fast" vs. "How fast is that dog running?" In these sentences "is" is not the main verb so it moves naturally as would any auxilliary including modals such as "can" or "will." It takes the position of complementizer (T -> C movement) where it would otherwise be null but still part of the essential structure in a statement ([(null C)] That dog [is (T)] running/[Is (C)] that dog [(moved T)] running?). But when "is" is a main verb, it is not a complementizer, or at least it does not appear to be.
The deeper tree structure of "That dog is friendly" seems to be far more complex than it first appears if it must allow for 1) a node with a null specifier component to appear on top of the whole sentence somewhere (perhaps a CP?) and 2) another node to lie above the VP (a TP?) that allows the V to move into the null T position (or something like it) only for the special case "to be."