get out from their radar when they notice you and you're safe.

How would the previous sentence be correctly capitalized?
Answer: Get out from their radar when they notice you and you're safe.
established in 2013, with the intention of maintaining the groups brand and marketing activities.

How would the previous sentence be correctly capitalized?
Answer: Established in 2013, with the intention of maintaining the Groups brand and marketing activities.
in 1940 hopf was on the list of the invited lecturers to the international congress of mathematicians to be held in cambridge, massachusetts.

How would the previous sentence be correctly capitalized?
Answer: In 1940 Hopf was on the list of the invited lecturers to the International Congress of Mathematicians to be held in Cambridge, Massachusetts.
this is a piece of the emperor.

How would the previous sentence be correctly capitalized?
Answer: This is a piece of the emperor.