Matrix is a sci-fi virtual-reality/cyberspace term.
Originally, matrix meant a womb, echoing the womb-like pods Neo and the others are kept in.
The science fiction meaning, however, is more recent, found in Doctor Who's Deadly Assassin (1976) as an equivalent of cyberspace:
How can you intercept thought patterns within the matrix itself?
Or as a VR-...
One of the definitions in the Merriam-Webster for Matrix is
something within or from which something else originates, develops, or takes form.
an enclosure within which something originates or develops (from the Latin for womb)
Another definition is:
an array of circuit elements (such as diodes and transistors) for performing a ...
The Wachowski's concept of the matrix is heavily influenced by Baudrillard's description of "hyperreality":
Baudrillard defined "hyperreality" as "the generation by models of a
real without origin or reality"; hyperreality is a representation,
a sign, without an original referent. According to Baudrillard, the
commodities in this theoretical state ...
Morpheus was being brief to avoid being traced. Going by generic crime tropes, people are often told to keep the line open for X amount of time so the source can be traced. It stands to reason that the same applies here, as Morpheus is handling this unsecure call the same way.
You can argue whether or not the machines should have more direct control over ...
As a matter of fact, oracles would allow Turing machines to go beyond logic, since they're able to solve problems in constant time; that relates them to imagination or freedom of will and thus to the Oracle in the movie. Of course, it's not an implementation, but it's plausible enough.