A 1000 $$ \times $$ 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).

P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.

(i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.

(ii) P is unable to row when someone else is in the boat.

(iii) Q is unable to row with anyone else except R.

(iv) Each person rowed for at least one trip.

(v) Only one person can row during a trip.

Who rowed twice?

"A common misconception among writers is that sentence structure mirrors thought; the more _________ the structure, the more complicated the ideas."

The word that best fills the blank in the above sentence is

The three roots of the equation f(x) = 0 are x = {-2, 0, 3}. What are the three values of x for which f(x -3) = 0?