Given: The preparation of potassium permanganate involves two steps. In the first step, manganese dioxide (\( \text{MnO}_2 \)) reacts with potassium hydroxide (KOH) and potassium nitrate (\( \text{KNO}_3 \)) to form potassium manganate (\( \text{K}_2\text{MnO}_4 \)).
The reaction is as follows: \[ \text{MnO}_2 + 4 \text{KOH} + 2 \text{KNO}_3 \to \text{K}_2\text{MnO}_4 + 2 \text{H}_2\text{O} \] - Manganese dioxide reacts with potassium hydroxide and potassium nitrate to produce potassium manganate and water.
The product of the first step is \( \boxed{\text{K}_2\text{MnO}_4} \), which corresponds to option (4).
The net current flowing in the given circuit is ___ A.
If the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) has equal roots, where \( a + c = 15 \) and \( b = \frac{36}{5} \), then \( a^2 + c^2 \) is equal to .