English translation: to be read and signed by the responsible persons
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Explanation: What it actually means that those responsible persons should read this list with their names and sign that they know that they were made responsible for fire safety. This is a standard bureaucratic procedure in Russia. Под росись literally means that they are to sign. Ознакомление means that they have to read what they need to sign.
I have changed my mind several times about this one. There is an almost 50-50 split between the answerers about who the 'otvetstvennyye litsa' are - those who are made responsible for fire safety, or 'key figures' (in Marfus' version) in the company hierarchy. The latter is of course a very common meaning of the phrase. There is, however, something very logical and persuasive about Ksenia's description of the process that makes me lean towards the former. And I've worked in institutions where we have had to read and sign memos asserting our responsibility for x y or z. Hope I've got this one right. 4 KudoZ points were awarded for this answer