Please capitalize where necessary: in 1939 he examined the homology of a compact lie group.
A: In 1939 he examined the homology of a compact Lie group.
Q: since the first space trip occurred not all that long ago, i believe that no one really had time to look for life as intense as it could have been.

A: Since the first space trip occurred not all that long ago, I believe that no one really had time to look for life as intense as it could have been.
Q: woe unto them that are mighty for drinking wine, and men valiant to mix strong drink;
A: Woe unto them that are mighty for drinking wine, and men valiant to mix strong drink;
Problem: rather than using normal, full-scale laboratory equipment, these experiments are carried out in a chewing-gum blister packet, from which the foil and the gum have been removed (see image).
Can you repeat this sentence, but capitalize it?
Answer: Rather than using normal, full-scale laboratory equipment, these experiments are carried out in a chewing-gum blister packet, from which the foil and the gum have been removed (see image).
Text: extension cable m12cm-extp-… fully compensated m12 thermocouple cables with pvc insulated cables and tpu over molded connectors (85°c max)

Correct capitalization: Extension Cable M12CM-EXTP-… Fully Compensated M12 Thermocouple cables with PVC insulated cables and TPU over molded connectors (85°C Max)
Text: follow us chevrolet to be official automotive partner of manchester united

Correct capitalization:
Follow Us Chevrolet to be Official Automotive Partner of Manchester United