Final answer:
No, the sky would not be dark in the daytime tomorrow if nuclear fusion in the sun's core suddenly stopped.
Step-by-step explanation:
If nuclear fusion in the sun's core suddenly stopped today, the sky would not be dark in the daytime tomorrow. The sunlight that we see on Earth does not come directly from the sun's core, but rather from the sun's photosphere, which is the visible surface of the sun. The energy produced by nuclear fusion in the sun's core takes a long time to reach the surface, so even if fusion stopped today, the sunlight from the photosphere would still reach us for several more years.