the chain of the order of dannebrog with insignia, gold with enamel and table-cut stones.

How would the previous sentence be correctly capitalized?
Answer: The Chain of the Order of Dannebrog with Insignia, gold with enamel and table-cut stones.
retractable clotheslines are becoming an increasingly popular way to dry your laundry.

How would the previous sentence be correctly capitalized?
Answer: Retractable Clotheslines are becoming an increasingly popular way to dry your laundry.
von koch was then appointed to the chair of pure mathematics at the kth.

How would the previous sentence be correctly capitalized?
Answer: Von Koch was then appointed to the chair of pure mathematics at the KTH.
ko samui is a tropical island as backpackers long thought they could keep a secret from the rest of the world.

How would the previous sentence be correctly capitalized?
Answer: Ko Samui is a tropical island as backpackers long thought they could keep a secret from the rest of the world.